diff --git a/doc/source/whatsnew/v2.2.0.rst b/doc/source/whatsnew/v2.2.0.rst
index acec8379ee5b3..908cd528dc11f 100644
--- a/doc/source/whatsnew/v2.2.0.rst
+++ b/doc/source/whatsnew/v2.2.0.rst
@@ -665,6 +665,7 @@ Reshaping
 - Bug in :func:`concat` ignoring ``sort`` parameter when passed :class:`DatetimeIndex` indexes (:issue:`54769`)
 - Bug in :func:`concat` renaming :class:`Series` when ``ignore_index=False`` (:issue:`15047`)
 - Bug in :func:`merge_asof` raising ``TypeError`` when ``by`` dtype is not ``object``, ``int64``, or ``uint64`` (:issue:`22794`)
+- Bug in :func:`merge_asof` raising incorrect error for string dtype (:issue:`56444`)
 - Bug in :func:`merge` returning columns in incorrect order when left and/or right is empty (:issue:`51929`)
 - Bug in :meth:`DataFrame.melt` where an exception was raised if ``var_name`` was not a string (:issue:`55948`)
 - Bug in :meth:`DataFrame.melt` where it would not preserve the datetime (:issue:`55254`)
diff --git a/pandas/core/reshape/merge.py b/pandas/core/reshape/merge.py
index f07c4fb8f7d5f..c43c16cded852 100644
--- a/pandas/core/reshape/merge.py
+++ b/pandas/core/reshape/merge.py
@@ -1986,7 +1986,12 @@ def _validate_left_right_on(self, left_on, right_on):
         else:
             ro_dtype = self.right.index.dtype
 
-        if is_object_dtype(lo_dtype) or is_object_dtype(ro_dtype):
+        if (
+            is_object_dtype(lo_dtype)
+            or is_object_dtype(ro_dtype)
+            or is_string_dtype(lo_dtype)
+            or is_string_dtype(ro_dtype)
+        ):
             raise MergeError(
                 f"Incompatible merge dtype, {repr(ro_dtype)} and "
                 f"{repr(lo_dtype)}, both sides must have numeric dtype"
diff --git a/pandas/tests/reshape/merge/test_merge_asof.py b/pandas/tests/reshape/merge/test_merge_asof.py
index 6d0a405430c9f..f6278e5e2f38b 100644
--- a/pandas/tests/reshape/merge/test_merge_asof.py
+++ b/pandas/tests/reshape/merge/test_merge_asof.py
@@ -11,6 +11,7 @@
     Index,
     Timedelta,
     merge_asof,
+    option_context,
     to_datetime,
 )
 import pandas._testing as tm
@@ -3372,6 +3373,9 @@ def test_left_index_right_index_tolerance(self, unit):
         tm.assert_frame_equal(result, expected)
 
 
+@pytest.mark.parametrize(
+    "infer_string", [False, pytest.param(True, marks=td.skip_if_no("pyarrow"))]
+)
 @pytest.mark.parametrize(
     "kwargs", [{"on": "x"}, {"left_index": True, "right_index": True}]
 )
@@ -3379,15 +3383,16 @@ def test_left_index_right_index_tolerance(self, unit):
     "data",
     [["2019-06-01 00:09:12", "2019-06-01 00:10:29"], [1.0, "2019-06-01 00:10:29"]],
 )
-def test_merge_asof_non_numerical_dtype(kwargs, data):
+def test_merge_asof_non_numerical_dtype(kwargs, data, infer_string):
     # GH#29130
-    left = pd.DataFrame({"x": data}, index=data)
-    right = pd.DataFrame({"x": data}, index=data)
-    with pytest.raises(
-        MergeError,
-        match=r"Incompatible merge dtype, .*, both sides must have numeric dtype",
-    ):
-        merge_asof(left, right, **kwargs)
+    with option_context("future.infer_string", infer_string):
+        left = pd.DataFrame({"x": data}, index=data)
+        right = pd.DataFrame({"x": data}, index=data)
+        with pytest.raises(
+            MergeError,
+            match=r"Incompatible merge dtype, .*, both sides must have numeric dtype",
+        ):
+            merge_asof(left, right, **kwargs)
 
 
 def test_merge_asof_non_numerical_dtype_object():