diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index b4b98ec0403a8..84f1fa6ad8086 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -302,8 +302,7 @@ Reshaping
 - Bug in :meth:`DataFrame.unstack` with missing levels led to incorrect index names (:issue:`37510`)
 - Bug in :func:`join` over :class:`MultiIndex` returned wrong result, when one of both indexes had only one level (:issue:`36909`)
 - Bug in :func:`concat` incorrectly casting to ``object`` dtype in some cases when one or more of the operands is empty (:issue:`38843`, :issue:`38907`)
--
-
+- :meth:`merge_asof` raises ``ValueError`` instead of cryptic ``TypeError`` in case of non-numerical merge columns (:issue:`29130`)
 
 Sparse
 ^^^^^^
diff --git a/pandas/core/reshape/merge.py b/pandas/core/reshape/merge.py
index ac5fc7cddf82a..1caf1a2a023da 100644
--- a/pandas/core/reshape/merge.py
+++ b/pandas/core/reshape/merge.py
@@ -1708,6 +1708,23 @@ def _validate_specification(self):
         if self.left_by is not None and self.right_by is None:
             raise MergeError("missing right_by")
 
+        # GH#29130 Check that merge keys do not have dtype object
+        lo_dtype = (
+            self.left[self.left_on[0]].dtype
+            if not self.left_index
+            else self.left.index.dtype
+        )
+        ro_dtype = (
+            self.right[self.right_on[0]].dtype
+            if not self.right_index
+            else self.right.index.dtype
+        )
+        if is_object_dtype(lo_dtype) or is_object_dtype(ro_dtype):
+            raise MergeError(
+                f"Incompatible merge dtype, {repr(ro_dtype)} and "
+                f"{repr(lo_dtype)}, both sides must have numeric dtype"
+            )
+
         # add 'by' to our key-list so we can have it in the
         # output as a key
         if self.left_by is not None:
diff --git a/pandas/tests/reshape/merge/test_merge_asof.py b/pandas/tests/reshape/merge/test_merge_asof.py
index 5cb7bdd603517..ecff63b495fbb 100644
--- a/pandas/tests/reshape/merge/test_merge_asof.py
+++ b/pandas/tests/reshape/merge/test_merge_asof.py
@@ -1168,7 +1168,7 @@ def test_on_float_by_int(self):
         tm.assert_frame_equal(result, expected)
 
     def test_merge_datatype_error_raises(self):
-        msg = r"incompatible merge keys \[0\] .*, must be the same type"
+        msg = r"Incompatible merge dtype, .*, both sides must have numeric dtype"
 
         left = pd.DataFrame({"left_val": [1, 5, 10], "a": ["a", "b", "c"]})
         right = pd.DataFrame({"right_val": [1, 2, 3, 6, 7], "a": [1, 2, 3, 6, 7]})
@@ -1373,3 +1373,39 @@ def test_left_index_right_index_tolerance(self):
             tolerance=Timedelta(seconds=0.5),
         )
         tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize(
+    "kwargs", [{"on": "x"}, {"left_index": True, "right_index": True}]
+)
+@pytest.mark.parametrize(
+    "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):
+    # 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",
+    ):
+        pd.merge_asof(left, right, **kwargs)
+
+
+def test_merge_asof_non_numerical_dtype_object():
+    # GH#29130
+    left = pd.DataFrame({"a": ["12", "13", "15"], "left_val1": ["a", "b", "c"]})
+    right = pd.DataFrame({"a": ["a", "b", "c"], "left_val": ["d", "e", "f"]})
+    with pytest.raises(
+        MergeError,
+        match=r"Incompatible merge dtype, .*, both sides must have numeric dtype",
+    ):
+        pd.merge_asof(
+            left,
+            right,
+            left_on="left_val1",
+            right_on="a",
+            left_by="a",
+            right_by="left_val",
+        )