diff --git a/moto/core/models.py b/moto/core/models.py
index 1597efc7b..ba4564e4a 100644
--- a/moto/core/models.py
+++ b/moto/core/models.py
@@ -184,6 +184,8 @@ class CallbackResponse(responses.CallbackResponse):
                 body = None
             elif isinstance(request.body, six.text_type):
                 body = six.BytesIO(six.b(request.body))
+            elif hasattr(request.body, "read"):
+                body = six.BytesIO(request.body.read())
             else:
                 body = six.BytesIO(request.body)
             req = Request.from_values(
diff --git a/tests/test_s3/test_s3.py b/tests/test_s3/test_s3.py
index 363ccc02d..1d1e83478 100644
--- a/tests/test_s3/test_s3.py
+++ b/tests/test_s3/test_s3.py
@@ -1040,6 +1040,22 @@ def test_s3_object_in_public_bucket_using_multiple_presigned_urls():
         assert response.status_code == 200, "Failed on req number {}".format(i)
 
 
+@mock_s3
+def test_streaming_upload_from_file_to_presigned_url():
+    s3 = boto3.resource("s3")
+    bucket = s3.Bucket("test-bucket")
+    bucket.create()
+    bucket.put_object(Body=b"ABCD", Key="file.txt")
+
+    params = {"Bucket": "test-bucket", "Key": "file.txt"}
+    presigned_url = boto3.client("s3").generate_presigned_url(
+        "put_object", params, ExpiresIn=900
+    )
+    with open(__file__, "rb") as f:
+        response = requests.get(presigned_url, data=f)
+    assert response.status_code == 200
+
+
 @mock_s3
 def test_s3_object_in_private_bucket():
     s3 = boto3.resource("s3")