diff --git a/newsfragments/5604.fixed.md b/newsfragments/5604.fixed.md
new file mode 100644
index 00000000000..6bc52a41a55
--- /dev/null
+++ b/newsfragments/5604.fixed.md
@@ -0,0 +1 @@
+Handle errors on `PyIterator` when calling `size_hint`
diff --git a/src/types/iterator.rs b/src/types/iterator.rs
index 62ab3bac742..2ab1bda1722 100644
--- a/src/types/iterator.rs
+++ b/src/types/iterator.rs
@@ -108,8 +108,15 @@ impl<'py> Iterator for Bound<'py, PyIterator> {
 
     #[cfg(not(Py_LIMITED_API))]
     fn size_hint(&self) -> (usize, Option<usize>) {
+        // SAFETY: `self` is a valid iterator object
         let hint = unsafe { ffi::PyObject_LengthHint(self.as_ptr(), 0) };
-        (hint.max(0) as usize, None)
+        if hint < 0 {
+            let py = self.py();
+            PyErr::fetch(py).write_unraisable(py, Some(self));
+            (0, None)
+        } else {
+            (hint as usize, None)
+        }
     }
 }
 
@@ -144,6 +151,8 @@ mod tests {
     #[cfg(all(not(PyPy), Py_3_10))]
     use crate::types::PyNone;
     use crate::types::{PyAnyMethods, PyDict, PyList, PyListMethods};
+    #[cfg(all(feature = "macros", Py_3_8, not(Py_LIMITED_API)))]
+    use crate::PyErr;
     use crate::{IntoPyObject, PyTypeInfo, Python};
 
     #[test]
@@ -392,6 +401,46 @@ def fibonacci(target):
         });
     }
 
+    #[test]
+    #[cfg(all(feature = "macros", Py_3_8, not(Py_LIMITED_API)))]
+    fn length_hint_error() {
+        #[crate::pyfunction(crate = "crate")]
+        fn test_size_hint(obj: &crate::Bound<'_, crate::PyAny>, should_error: bool) {
+            let iter = obj.cast::<PyIterator>().unwrap();
+            crate::test_utils::UnraisableCapture::enter(obj.py(), |capture| {
+                assert_eq!((0, None), iter.size_hint());
+                assert_eq!(should_error, capture.take_capture().is_some());
+            });
+            assert!(PyErr::take(obj.py()).is_none());
+        }
+
+        Python::attach(|py| {
+            let test_size_hint = crate::wrap_pyfunction!(test_size_hint, py).unwrap();
+            crate::py_run!(
+                py,
+                test_size_hint,
+                r#"
+                    class NoHintIter:
+                        def __next__(self):
+                            raise StopIteration
+
+                        def __length_hint__(self):
+                            return NotImplemented
+
+                    class ErrorHintIter:
+                        def __next__(self):
+                            raise StopIteration
+
+                        def __length_hint__(self):
+                            raise ValueError("bad hint impl")
+
+                    test_size_hint(NoHintIter(), False)
+                    test_size_hint(ErrorHintIter(), True)
+                "#
+            );
+        });
+    }
+
     #[test]
     fn test_type_object() {
         Python::attach(|py| {