diff --git a/moto/cloudwatch/exceptions.py b/moto/cloudwatch/exceptions.py
index c7bfa29b5..4196cc994 100644
--- a/moto/cloudwatch/exceptions.py
+++ b/moto/cloudwatch/exceptions.py
@@ -15,6 +15,13 @@ class InvalidParameterValue(RESTError):
         super().__init__(__class__.__name__, message)
 
 
+class InvalidParameterCombination(RESTError):
+    code = 400
+
+    def __init__(self, message):
+        super().__init__(__class__.__name__, message)
+
+
 class ResourceNotFound(RESTError):
     code = 404
 
diff --git a/moto/cloudwatch/responses.py b/moto/cloudwatch/responses.py
index 4c5fd265f..778e533bf 100644
--- a/moto/cloudwatch/responses.py
+++ b/moto/cloudwatch/responses.py
@@ -5,6 +5,7 @@ from dateutil.parser import parse as dtparse
 from moto.core.responses import BaseResponse
 from moto.core.utils import amzn_request_id
 from .models import cloudwatch_backends, MetricDataQuery, MetricStat, Metric, Dimension
+from .exceptions import InvalidParameterCombination
 
 
 class CloudWatchResponse(BaseResponse):
@@ -187,9 +188,8 @@ class CloudWatchResponse(BaseResponse):
         unit = self._get_param("Unit")
         extended_statistics = self._get_param("ExtendedStatistics")
 
-        # TODO: this should instead throw InvalidParameterCombination
         if not statistics and not extended_statistics:
-            raise NotImplementedError(
+            raise InvalidParameterCombination(
                 "Must specify either Statistics or ExtendedStatistics"
             )
 
diff --git a/tests/test_cloudwatch/test_cloudwatch_boto3.py b/tests/test_cloudwatch/test_cloudwatch_boto3.py
index 35f4db783..ebe0eb495 100644
--- a/tests/test_cloudwatch/test_cloudwatch_boto3.py
+++ b/tests/test_cloudwatch/test_cloudwatch_boto3.py
@@ -105,6 +105,31 @@ def test_get_metric_statistics():
     datapoint["Sum"].should.equal(1.5)
 
 
+@mock_cloudwatch
+def test_get_metric_invalid_parameter_combination():
+    conn = boto3.client("cloudwatch", region_name="us-east-1")
+    utc_now = datetime.now(tz=pytz.utc)
+
+    conn.put_metric_data(
+        Namespace="tester",
+        MetricData=[dict(MetricName="metric", Value=1.5, Timestamp=utc_now)],
+    )
+
+    with pytest.raises(ClientError) as exc:
+        # make request without both statistics or extended statistics parameters
+        conn.get_metric_statistics(
+            Namespace="tester",
+            MetricName="metric",
+            StartTime=utc_now - timedelta(seconds=60),
+            EndTime=utc_now + timedelta(seconds=60),
+            Period=60,
+        )
+
+    err = exc.value.response["Error"]
+    err["Code"].should.equal("InvalidParameterCombination")
+    err["Message"].should.equal("Must specify either Statistics or ExtendedStatistics")
+
+
 @mock_cloudwatch
 def test_get_metric_statistics_dimensions():
     conn = boto3.client("cloudwatch", region_name="us-east-1")