diff --git a/src/sagemaker/model_monitor/monitoring_files.py b/src/sagemaker/model_monitor/monitoring_files.py
index 6768a5270f..a4863377ab 100644
--- a/src/sagemaker/model_monitor/monitoring_files.py
+++ b/src/sagemaker/model_monitor/monitoring_files.py
@@ -362,10 +362,9 @@ def set_monitoring(self, enable_monitoring, feature_name=None):
         else:
             for feature in self.body_dict["features"]:
                 if feature["name"] == feature_name:
-                    string_constraints = feature["string_constraints"]
-                    if string_constraints.get("monitoring_config_overrides") is None:
-                        string_constraints["monitoring_config_overrides"] = {}
-                    string_constraints["monitoring_config_overrides"]["evaluate_constraints"] = flag
+                    if feature.get("monitoring_config_overrides") is None:
+                        feature["monitoring_config_overrides"] = {}
+                    feature["monitoring_config_overrides"]["evaluate_constraints"] = flag
 
 
 class ConstraintViolations(ModelMonitoringFile):
diff --git a/tests/unit/sagemaker/monitor/test_monitoring_files.py b/tests/unit/sagemaker/monitor/test_monitoring_files.py
new file mode 100644
index 0000000000..cdc0174044
--- /dev/null
+++ b/tests/unit/sagemaker/monitor/test_monitoring_files.py
@@ -0,0 +1,114 @@
+# Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License"). You
+# may not use this file except in compliance with the License. A copy of
+# the License is located at
+#
+#     http://aws.amazon.com/apache2.0/
+#
+# or in the "license" file accompanying this file. This file is
+# distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF
+# ANY KIND, either express or implied. See the License for the specific
+# language governing permissions and limitations under the License.
+"""Unit tests for the Constraints.set_monitoring feature-level override."""
+from __future__ import absolute_import
+
+import pytest
+
+from sagemaker.model_monitor.monitoring_files import Constraints
+
+CONSTRAINTS_S3_URI = "s3://bucket/constraints.json"
+
+
+def _body_dict():
+    """A constraints body with one non-string (binary/integral) and one string feature."""
+    return {
+        "version": 0.0,
+        "features": [
+            {
+                "name": "Churn",
+                "inferred_type": "Integral",
+                "num_constraints": {"is_non_negative": True},
+            },
+            {
+                "name": "State",
+                "inferred_type": "String",
+                "string_constraints": {"domains": ["OH", "NJ"]},
+            },
+        ],
+        "monitoring_config": {"evaluate_constraints": "Enabled"},
+    }
+
+
+def _make_constraints():
+    return Constraints(body_dict=_body_dict(), constraints_file_s3_uri=CONSTRAINTS_S3_URI)
+
+
+def _feature(constraints, name):
+    return next(f for f in constraints.body_dict["features"] if f["name"] == name)
+
+
+def test_set_monitoring_disables_non_string_feature():
+    # Regression test for GitHub issue #2745: set_monitoring must work for a
+    # non-string (e.g. binary/integral) feature that has no string_constraints section.
+    constraints = _make_constraints()
+
+    constraints.set_monitoring(False, feature_name="Churn")
+
+    churn = _feature(constraints, "Churn")
+    assert churn["monitoring_config_overrides"] == {"evaluate_constraints": "Disabled"}
+    # The override must live at the feature level, not nested inside num_constraints.
+    assert "monitoring_config_overrides" not in churn["num_constraints"]
+
+
+def test_set_monitoring_override_is_feature_level_for_string_feature():
+    # Even for a string feature, the override belongs at the feature level (per the
+    # constraints.json schema), not inside the string_constraints section.
+    constraints = _make_constraints()
+
+    constraints.set_monitoring(False, feature_name="State")
+
+    state = _feature(constraints, "State")
+    assert state["monitoring_config_overrides"] == {"evaluate_constraints": "Disabled"}
+    assert "monitoring_config_overrides" not in state["string_constraints"]
+
+
+def test_set_monitoring_enable_maps_to_enabled():
+    constraints = _make_constraints()
+
+    constraints.set_monitoring(True, feature_name="Churn")
+
+    assert _feature(constraints, "Churn")["monitoring_config_overrides"] == {
+        "evaluate_constraints": "Enabled"
+    }
+
+
+def test_set_monitoring_preserves_existing_overrides():
+    body = _body_dict()
+    body["features"][0]["monitoring_config_overrides"] = {"some_other_flag": "keep"}
+    constraints = Constraints(body_dict=body, constraints_file_s3_uri=CONSTRAINTS_S3_URI)
+
+    constraints.set_monitoring(False, feature_name="Churn")
+
+    overrides = _feature(constraints, "Churn")["monitoring_config_overrides"]
+    assert overrides == {"some_other_flag": "keep", "evaluate_constraints": "Disabled"}
+
+
+def test_set_monitoring_without_feature_name_sets_top_level_flag():
+    constraints = _make_constraints()
+
+    constraints.set_monitoring(False)
+
+    assert constraints.body_dict["monitoring_config"]["evaluate_constraints"] == "Disabled"
+
+
+@pytest.mark.parametrize("enable,expected", [(True, "Enabled"), (False, "Disabled")])
+def test_monitoring_api_map(enable, expected):
+    constraints = _make_constraints()
+
+    constraints.set_monitoring(enable, feature_name="Churn")
+
+    assert (
+        _feature(constraints, "Churn")["monitoring_config_overrides"]["evaluate_constraints"]
+        == expected
+    )