diff --git a/ignite/metrics/metric.py b/ignite/metrics/metric.py
index 0cbab97aaffa..19357e49876b 100644
--- a/ignite/metrics/metric.py
+++ b/ignite/metrics/metric.py
@@ -82,7 +82,9 @@ def compute(self) -> Any:
         This is called at the end of each epoch.
 
         Returns:
-            Any: the actual quantity of interest.
+            Any: the actual quantity of interest. However, if a :class:`~collections.abc.Mapping` is returned,
+                 it will be (shallow) flattened into `engine.state.metrics` when
+                 :func:`~ignite.metrics.Metric.completed` is called.
 
         Raises:
             NotComputableError: raised when the metric cannot be computed.
@@ -137,9 +139,14 @@ def iteration_completed(self, engine: Engine) -> None:
 
     def completed(self, engine: Engine, name: str) -> None:
         result = self.compute()
-        if torch.is_tensor(result) and len(result.shape) == 0:
-            result = result.item()
-        engine.state.metrics[name] = result
+        if isinstance(result, Mapping):
+            for key, value in result.items():
+                engine.state.metrics[key] = value
+        else:
+            if isinstance(result, torch.Tensor) and len(result.size()) == 0:
+                result = result.item()
+
+            engine.state.metrics[name] = result
 
     def attach(self, engine: Engine, name: str) -> None:
         """
diff --git a/tests/ignite/metrics/test_metric.py b/tests/ignite/metrics/test_metric.py
index 7d90ad9e27c9..198e4c969720 100644
--- a/tests/ignite/metrics/test_metric.py
+++ b/tests/ignite/metrics/test_metric.py
@@ -1,3 +1,4 @@
+import numbers
 import os
 import sys
 
@@ -632,3 +633,37 @@ def test_multinode_distrib_gpu(distributed_context_multi_node_nccl):
     device = "cuda:{}".format(distributed_context_multi_node_nccl["local_rank"])
     _test_distrib__sync_all_reduce(device)
     _test_distrib_sync_all_reduce_decorator(device)
+
+
+def test_completed():
+    class DummyMetric(Metric):
+        def reset(self):
+            pass
+
+        def compute(self):
+            pass
+
+        def update(self, output):
+            pass
+
+    m = DummyMetric()
+
+    # tensor
+    engine = MagicMock(state=State(metrics={}))
+    m.compute = MagicMock(return_value=torch.tensor(1.0))
+    m.completed(engine, "metric")
+    assert engine.state.metrics == {"metric": 1.0}
+    assert isinstance(engine.state.metrics["metric"], numbers.Number)
+
+    # mapping
+    engine = MagicMock(state=State(metrics={}))
+    metrics = {"foo": 1, "bar": torch.tensor(2.0), "baz": {"qux": "quux"}}
+    m.compute = MagicMock(return_value=metrics)
+    m.completed(engine, "metric")
+    assert engine.state.metrics == metrics
+
+    # other
+    engine = MagicMock(state=State(metrics={}))
+    m.compute = MagicMock(return_value="foo")
+    m.completed(engine, "metric")
+    assert engine.state.metrics == {"metric": "foo"}