diff --git a/numpy/_core/src/multiarray/stringdtype/static_string.c b/numpy/_core/src/multiarray/stringdtype/static_string.c
index 1c29bbb67f7e..89b53bcb8538 100644
--- a/numpy/_core/src/multiarray/stringdtype/static_string.c
+++ b/numpy/_core/src/multiarray/stringdtype/static_string.c
@@ -478,7 +478,7 @@ heap_or_arena_allocate(npy_string_allocator *allocator,
         if (*flags == 0) {
             // string isn't previously allocated, so add to existing arena allocation
             char *ret = arena_malloc(arena, allocator->realloc, sizeof(char) * size);
-            if (size < NPY_MEDIUM_STRING_MAX_SIZE) {
+            if (size <= NPY_MEDIUM_STRING_MAX_SIZE) {
                 *flags = NPY_STRING_INITIALIZED;
             }
             else {
diff --git a/numpy/_core/tests/test_stringdtype.py b/numpy/_core/tests/test_stringdtype.py
index 9bab810d4421..1c2b606dedf3 100644
--- a/numpy/_core/tests/test_stringdtype.py
+++ b/numpy/_core/tests/test_stringdtype.py
@@ -1193,6 +1193,24 @@ def test_growing_strings(dtype):
     assert_array_equal(arr, uarr)
 
 
+def test_assign_medium_strings():
+    # see gh-29261
+    N = 9
+    src = np.array(
+        (
+            ['0' * 256] * 3 + ['0' * 255] + ['0' * 256] + ['0' * 255] +
+            ['0' * 256] * 2 + ['0' * 255]
+        ), dtype='T')
+    dst = np.array(
+        (
+            ['0' * 255] + ['0' * 256] * 2 + ['0' * 255] + ['0' * 256] +
+            ['0' * 255] + [''] * 5
+        ), dtype='T')
+
+    dst[1:N + 1] = src
+    assert_array_equal(dst[1:N + 1], src)
+
+
 UFUNC_TEST_DATA = [
     "hello" * 10,
     "Ae¢☃€ 😊" * 20,