diff --git a/moto/cloudwatch/models.py b/moto/cloudwatch/models.py
index 4546eccce..009492e19 100644
--- a/moto/cloudwatch/models.py
+++ b/moto/cloudwatch/models.py
@@ -168,7 +168,7 @@ def are_dimensions_same(metric_dimensions, dimensions):
 
 
 class MetricDatum(BaseModel):
-    def __init__(self, namespace, name, value, dimensions, timestamp):
+    def __init__(self, namespace, name, value, dimensions, timestamp, unit=None):
         self.namespace = namespace
         self.name = name
         self.value = value
@@ -176,6 +176,7 @@ class MetricDatum(BaseModel):
         self.dimensions = [
             Dimension(dimension["Name"], dimension["Value"]) for dimension in dimensions
         ]
+        self.unit = unit
 
     def filter(self, namespace, name, dimensions, already_present_metrics):
         if namespace and namespace != self.namespace:
@@ -385,6 +386,7 @@ class CloudWatchBackend(BaseBackend):
                     float(metric_member.get("Value", 0)),
                     metric_member.get("Dimensions.member", _EMPTY_LIST),
                     timestamp,
+                    metric_member.get("Unit"),
                 )
             )
 
@@ -449,7 +451,7 @@ class CloudWatchBackend(BaseBackend):
         return results
 
     def get_metric_statistics(
-        self, namespace, metric_name, start_time, end_time, period, stats
+        self, namespace, metric_name, start_time, end_time, period, stats, unit=None
     ):
         period_delta = timedelta(seconds=period)
         filtered_data = [
@@ -460,6 +462,9 @@ class CloudWatchBackend(BaseBackend):
             and start_time <= md.timestamp <= end_time
         ]
 
+        if unit:
+            filtered_data = [md for md in filtered_data if md.unit == unit]
+
         # earliest to oldest
         filtered_data = sorted(filtered_data, key=lambda x: x.timestamp)
         if not filtered_data:
diff --git a/moto/cloudwatch/responses.py b/moto/cloudwatch/responses.py
index 063dff8b6..35430cc9e 100644
--- a/moto/cloudwatch/responses.py
+++ b/moto/cloudwatch/responses.py
@@ -119,7 +119,6 @@ class CloudWatchResponse(BaseResponse):
     def put_metric_data(self):
         namespace = self._get_param("Namespace")
         metric_data = self._get_multi_param("MetricData.member")
-
         self.cloudwatch_backend.put_metric_data(namespace, metric_data)
         template = self.response_template(PUT_METRIC_DATA_TEMPLATE)
         return template.render()
@@ -151,7 +150,7 @@ class CloudWatchResponse(BaseResponse):
         unit = self._get_param("Unit")
         extended_statistics = self._get_param("ExtendedStatistics")
         dimensions = self._get_param("Dimensions")
-        if unit or extended_statistics or dimensions:
+        if extended_statistics or dimensions:
             raise NotImplementedError()
 
         # TODO: this should instead throw InvalidParameterCombination
@@ -161,7 +160,7 @@ class CloudWatchResponse(BaseResponse):
             )
 
         datapoints = self.cloudwatch_backend.get_metric_statistics(
-            namespace, metric_name, start_time, end_time, period, statistics
+            namespace, metric_name, start_time, end_time, period, statistics, unit
         )
         template = self.response_template(GET_METRIC_STATISTICS_TEMPLATE)
         return template.render(label=metric_name, datapoints=datapoints)
@@ -514,7 +513,9 @@ GET_METRIC_STATISTICS_TEMPLATE = """<GetMetricStatisticsResponse xmlns="http://m
               {% endif %}
 
               <Timestamp>{{ datapoint.timestamp }}</Timestamp>
+              {% if datapoint.unit is not none %}
               <Unit>{{ datapoint.unit }}</Unit>
+              {% endif %}
             </member>
         {% endfor %}
       </Datapoints>
diff --git a/tests/test_cloudwatch/test_cloudwatch.py b/tests/test_cloudwatch/test_cloudwatch.py
index 92e1cd498..eb042c0e0 100644
--- a/tests/test_cloudwatch/test_cloudwatch.py
+++ b/tests/test_cloudwatch/test_cloudwatch.py
@@ -158,6 +158,7 @@ def test_get_metric_statistics():
         value=1.5,
         dimensions={"InstanceId": ["i-0123456,i-0123457"]},
         timestamp=metric_timestamp,
+        unit="Count",
     )
 
     metric_kwargs = dict(
@@ -167,6 +168,7 @@ def test_get_metric_statistics():
         end_time=datetime.now(),
         period=3600,
         statistics=["Minimum"],
+        unit="Count",
     )
 
     datapoints = conn.get_metric_statistics(**metric_kwargs)
@@ -175,6 +177,19 @@ def test_get_metric_statistics():
     datapoint.should.have.key("Minimum").which.should.equal(1.5)
     datapoint.should.have.key("Timestamp").which.should.equal(metric_timestamp)
 
+    metric_kwargs = dict(
+        namespace="tester",
+        metric_name="metric",
+        start_time=metric_timestamp,
+        end_time=datetime.now(),
+        period=3600,
+        statistics=["Minimum"],
+        unit="Percent",
+    )
+
+    datapoints = conn.get_metric_statistics(**metric_kwargs)
+    datapoints.should.have.length_of(0)
+
 
 # TODO: THIS IS CURRENTLY BROKEN!
 # @mock_s3_deprecated