diff --git a/moto/s3/responses.py b/moto/s3/responses.py
index 5285cd975..f10bd6500 100644
--- a/moto/s3/responses.py
+++ b/moto/s3/responses.py
@@ -1319,7 +1319,10 @@ class S3Response(BaseResponse):
             response_headers["x-amz-version-id"] = key.version_id
 
         if key.storage_class in ARCHIVE_STORAGE_CLASSES:
-            raise InvalidObjectState(storage_class=key.storage_class)
+            if 'ongoing-request="false"' not in key.response_dict.get(
+                "x-amz-restore", ""
+            ):
+                raise InvalidObjectState(storage_class=key.storage_class)
         if if_unmodified_since:
             if_unmodified_since = str_to_rfc_1123_datetime(if_unmodified_since)
             if key.last_modified.replace(microsecond=0) > if_unmodified_since:
diff --git a/tests/test_s3/test_s3_storageclass.py b/tests/test_s3/test_s3_storageclass.py
index 4c71a6b33..c0fa60cd6 100644
--- a/tests/test_s3/test_s3_storageclass.py
+++ b/tests/test_s3/test_s3_storageclass.py
@@ -231,8 +231,18 @@ def test_s3_copy_object_for_deep_archive_storage_class_restored():
         Bucket="Bucket", Key="First_Object", Body="Body", StorageClass="DEEP_ARCHIVE"
     )
 
+    with pytest.raises(ClientError) as exc:
+        s3.get_object(Bucket="Bucket", Key="First_Object")
+    err = exc.value.response["Error"]
+    err["Code"].should.equal("InvalidObjectState")
+    err["Message"].should.equal(
+        "The operation is not valid for the object's storage class"
+    )
+    err["StorageClass"].should.equal("DEEP_ARCHIVE")
+
     s3.create_bucket(Bucket="Bucket2")
     s3.restore_object(Bucket="Bucket", Key="First_Object", RestoreRequest={"Days": 123})
+    s3.get_object(Bucket="Bucket", Key="First_Object")
 
     s3.copy_object(
         CopySource={"Bucket": "Bucket", "Key": "First_Object"},