diff --git a/storages/backends/s3.py b/storages/backends/s3.py
index 3edc3c9a..66f7a0cf 100644
--- a/storages/backends/s3.py
+++ b/storages/backends/s3.py
@@ -535,7 +535,12 @@ def listdir(self, name):
 
     def size(self, name):
         name = self._normalize_name(clean_name(name))
-        return self.bucket.Object(name).content_length
+        try:
+            return self.bucket.Object(name).content_length
+        except ClientError as err:
+            if err.response["ResponseMetadata"]["HTTPStatusCode"] == 404:
+                raise FileNotFoundError("File does not exist: %s" % name)
+            raise  # Let it bubble up if it was some other error
 
     def _get_write_parameters(self, name, content=None):
         params = self.get_object_parameters(name)
diff --git a/tests/test_s3.py b/tests/test_s3.py
index 7d1e7f5f..6f43980a 100644
--- a/tests/test_s3.py
+++ b/tests/test_s3.py
@@ -647,6 +647,17 @@ def test_storage_size(self):
         name = "file.txt"
         self.assertEqual(self.storage.size(name), obj.content_length)
 
+    def test_storage_size_not_exists(self):
+        self.storage.bucket.Object.side_effect = ClientError(
+            {"Error": {}, "ResponseMetadata": {"HTTPStatusCode": 404}},
+            "HeadObject",
+        )
+        name = "file.txt"
+        with self.assertRaisesMessage(
+            FileNotFoundError, "File does not exist: file.txt"
+        ):
+            self.storage.size(name)
+
     def test_storage_mtime(self):
         # Test both USE_TZ cases
         for use_tz in (True, False):