diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 8e3ebc7816fed..19c94fa4104d7 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -638,7 +638,6 @@ def from_product(
                     (2, 'purple')],
                    names=['number', 'color'])
         """
-        from pandas.core.reshape.util import cartesian_product
 
         if not is_list_like(iterables):
             raise TypeError("Input must be a list / sequence of iterables.")
@@ -4105,3 +4104,60 @@ def _require_listlike(level, arr, arrname: str):
         if not is_list_like(arr) or not is_list_like(arr[0]):
             raise TypeError(f"{arrname} must be list of lists-like")
     return level, arr
+
+
+def cartesian_product(X: list[np.ndarray]) -> list[np.ndarray]:
+    """
+    Numpy version of itertools.product.
+    Sometimes faster (for large inputs)...
+
+    Parameters
+    ----------
+    X : list-like of list-likes
+
+    Returns
+    -------
+    product : list of ndarrays
+
+    Examples
+    --------
+    >>> cartesian_product([list("ABC"), [1, 2]])
+    [array(['A', 'A', 'B', 'B', 'C', 'C'], dtype='<U1'), array([1, 2, 1, 2, 1, 2])]
+
+    See Also
+    --------
+    itertools.product : Cartesian product of input iterables.  Equivalent to
+        nested for-loops.
+    """
+    msg = "Input must be a list-like of list-likes"
+    if not is_list_like(X):
+        raise TypeError(msg)
+    for x in X:
+        if not is_list_like(x):
+            raise TypeError(msg)
+
+    if len(X) == 0:
+        return []
+
+    lenX = np.fromiter((len(x) for x in X), dtype=np.intp)
+    cumprodX = np.cumprod(lenX)
+
+    if np.any(cumprodX < 0):
+        raise ValueError("Product space too large to allocate arrays!")
+
+    a = np.roll(cumprodX, 1)
+    a[0] = 1
+
+    if cumprodX[-1] != 0:
+        b = cumprodX[-1] / cumprodX
+    else:
+        # if any factor is empty, the cartesian product is empty
+        b = np.zeros_like(cumprodX)
+
+    return [
+        np.tile(
+            np.repeat(x, b[i]),
+            np.prod(a[i]),
+        )
+        for i, x in enumerate(X)
+    ]
diff --git a/pandas/core/reshape/melt.py b/pandas/core/reshape/melt.py
index 8756d0ad003d7..bfd8e3ccd2f7c 100644
--- a/pandas/core/reshape/melt.py
+++ b/pandas/core/reshape/melt.py
@@ -15,7 +15,6 @@
 import pandas.core.algorithms as algos
 from pandas.core.indexes.api import MultiIndex
 from pandas.core.reshape.concat import concat
-from pandas.core.reshape.util import tile_compat
 from pandas.core.tools.numeric import to_numeric
 
 if TYPE_CHECKING:
@@ -266,7 +265,8 @@ def melt(
     result = frame._constructor(mdata, columns=mcolumns)
 
     if not ignore_index:
-        result.index = tile_compat(frame.index, num_cols_adjusted)
+        taker = np.tile(np.arange(len(frame)), num_cols_adjusted)
+        result.index = frame.index.take(taker)
 
     return result
 
diff --git a/pandas/core/reshape/pivot.py b/pandas/core/reshape/pivot.py
index 0d9e9f520cbea..0886aad310034 100644
--- a/pandas/core/reshape/pivot.py
+++ b/pandas/core/reshape/pivot.py
@@ -31,7 +31,6 @@
     get_objs_combined_axis,
 )
 from pandas.core.reshape.concat import concat
-from pandas.core.reshape.util import cartesian_product
 from pandas.core.series import Series
 
 if TYPE_CHECKING:
@@ -358,15 +357,11 @@ def __internal_pivot_table(
 
     if not dropna:
         if isinstance(table.index, MultiIndex):
-            m = MultiIndex.from_arrays(
-                cartesian_product(table.index.levels), names=table.index.names
-            )
+            m = MultiIndex.from_product(table.index.levels, names=table.index.names)
             table = table.reindex(m, axis=0, fill_value=fill_value)
 
         if isinstance(table.columns, MultiIndex):
-            m = MultiIndex.from_arrays(
-                cartesian_product(table.columns.levels), names=table.columns.names
-            )
+            m = MultiIndex.from_product(table.columns.levels, names=table.columns.names)
             table = table.reindex(m, axis=1, fill_value=fill_value)
 
     if sort is True and isinstance(table, ABCDataFrame):
diff --git a/pandas/core/reshape/util.py b/pandas/core/reshape/util.py
deleted file mode 100644
index 0f1fbc662e1a6..0000000000000
--- a/pandas/core/reshape/util.py
+++ /dev/null
@@ -1,85 +0,0 @@
-from __future__ import annotations
-
-from typing import TYPE_CHECKING
-
-import numpy as np
-
-from pandas.core.dtypes.common import is_list_like
-
-if TYPE_CHECKING:
-    from pandas._typing import NumpyIndexT
-
-
-def cartesian_product(X) -> list[np.ndarray]:
-    """
-    Numpy version of itertools.product.
-    Sometimes faster (for large inputs)...
-
-    Parameters
-    ----------
-    X : list-like of list-likes
-
-    Returns
-    -------
-    product : list of ndarrays
-
-    Examples
-    --------
-    >>> cartesian_product([list("ABC"), [1, 2]])
-    [array(['A', 'A', 'B', 'B', 'C', 'C'], dtype='<U1'), array([1, 2, 1, 2, 1, 2])]
-
-    See Also
-    --------
-    itertools.product : Cartesian product of input iterables.  Equivalent to
-        nested for-loops.
-    """
-    msg = "Input must be a list-like of list-likes"
-    if not is_list_like(X):
-        raise TypeError(msg)
-    for x in X:
-        if not is_list_like(x):
-            raise TypeError(msg)
-
-    if len(X) == 0:
-        return []
-
-    lenX = np.fromiter((len(x) for x in X), dtype=np.intp)
-    cumprodX = np.cumprod(lenX)
-
-    if np.any(cumprodX < 0):
-        raise ValueError("Product space too large to allocate arrays!")
-
-    a = np.roll(cumprodX, 1)
-    a[0] = 1
-
-    if cumprodX[-1] != 0:
-        b = cumprodX[-1] / cumprodX
-    else:
-        # if any factor is empty, the cartesian product is empty
-        b = np.zeros_like(cumprodX)
-
-    # error: Argument of type "int_" cannot be assigned to parameter "num" of
-    # type "int" in function "tile_compat"
-    return [
-        tile_compat(
-            np.repeat(x, b[i]),
-            np.prod(a[i]),
-        )
-        for i, x in enumerate(X)
-    ]
-
-
-def tile_compat(arr: NumpyIndexT, num: int) -> NumpyIndexT:
-    """
-    Index compat for np.tile.
-
-    Notes
-    -----
-    Does not support multi-dimensional `num`.
-    """
-    if isinstance(arr, np.ndarray):
-        return np.tile(arr, num)
-
-    # Otherwise we have an Index
-    taker = np.tile(np.arange(len(arr)), num)
-    return arr.take(taker)
diff --git a/pandas/tests/reshape/test_util.py b/pandas/tests/indexes/multi/test_util.py
similarity index 78%
rename from pandas/tests/reshape/test_util.py
rename to pandas/tests/indexes/multi/test_util.py
index d2971db3d7aa2..68792ce53f04e 100644
--- a/pandas/tests/reshape/test_util.py
+++ b/pandas/tests/indexes/multi/test_util.py
@@ -6,7 +6,7 @@
     date_range,
 )
 import pandas._testing as tm
-from pandas.core.reshape.util import cartesian_product
+from pandas.core.indexes.multi import cartesian_product
 
 
 class TestCartesianProduct:
@@ -28,22 +28,6 @@ def test_datetimeindex(self):
         tm.assert_index_equal(result1, expected1)
         tm.assert_index_equal(result2, expected2)
 
-    def test_tzaware_retained(self):
-        x = date_range("2000-01-01", periods=2, tz="US/Pacific")
-        y = np.array([3, 4])
-        result1, result2 = cartesian_product([x, y])
-
-        expected = x.repeat(2)
-        tm.assert_index_equal(result1, expected)
-
-    def test_tzaware_retained_categorical(self):
-        x = date_range("2000-01-01", periods=2, tz="US/Pacific").astype("category")
-        y = np.array([3, 4])
-        result1, result2 = cartesian_product([x, y])
-
-        expected = x.repeat(2)
-        tm.assert_index_equal(result1, expected)
-
     @pytest.mark.parametrize("x, y", [[[], []], [[0, 1], []], [[], ["a", "b", "c"]]])
     def test_empty(self, x, y):
         # product of empty factors