diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 32c98fbf9d655..3de65fe6f682c 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -50,6 +50,7 @@ Other enhancements
 - :meth:`DataFrame.pivot_table` and :func:`pivot_table` now allow the passing of keyword arguments to ``aggfunc`` through ``**kwargs`` (:issue:`57884`)
 - :meth:`Series.cummin` and :meth:`Series.cummax` now supports :class:`CategoricalDtype` (:issue:`52335`)
 - :meth:`Series.plot` now correctly handle the ``ylabel`` parameter for pie charts, allowing for explicit control over the y-axis label (:issue:`58239`)
+- Multiplying two :class:`DateOffset` objects will now raise a ``TypeError`` instead of a ``RecursionError`` (:issue:`59442`)
 - Restore support for reading Stata 104-format and enable reading 103-format dta files (:issue:`58554`)
 - Support reading Stata 102-format (Stata 1) dta files (:issue:`58978`)
 - Support reading Stata 110-format (Stata 7) dta files (:issue:`47176`)
diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index fd1bb3fe3e173..554c4f109f1c5 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -491,6 +491,12 @@ cdef class BaseOffset:
         elif is_integer_object(other):
             return type(self)(n=other * self.n, normalize=self.normalize,
                               **self.kwds)
+        elif isinstance(other, BaseOffset):
+            # Otherwise raises RecurrsionError due to __rmul__
+            raise TypeError(
+                f"Cannot multiply {type(self).__name__} with "
+                f"{type(other).__name__}."
+            )
         return NotImplemented
 
     def __rmul__(self, other):
diff --git a/pandas/tests/tseries/offsets/test_offsets.py b/pandas/tests/tseries/offsets/test_offsets.py
index d19717e87c7d2..d0192c12f9518 100644
--- a/pandas/tests/tseries/offsets/test_offsets.py
+++ b/pandas/tests/tseries/offsets/test_offsets.py
@@ -1182,3 +1182,10 @@ def test_is_yqm_start_end():
 
     for ts, value in tests:
         assert ts == value
+
+
+@pytest.mark.parametrize("left", [DateOffset(1), Nano(1)])
+@pytest.mark.parametrize("right", [DateOffset(1), Nano(1)])
+def test_multiply_dateoffset_typeerror(left, right):
+    with pytest.raises(TypeError, match="Cannot multiply"):
+        left * right