diff --git a/storage/grpc_client.go b/storage/grpc_client.go
index df1ada07b55..742d0900651 100644
--- a/storage/grpc_client.go
+++ b/storage/grpc_client.go
@@ -893,6 +893,11 @@ func (c *grpcStorageClient) NewRangeReader(ctx context.Context, params *newRange
 			}
 
 			msg, err = stream.Recv()
+			// These types of errors show up on the Recv call, rather than the
+			// initialization of the stream via ReadObject above.
+			if s, ok := status.FromError(err); ok && s.Code() == codes.NotFound {
+				return ErrObjectNotExist
+			}
 
 			return err
 		}, s.retry, s.idempotent, setRetryHeaderGRPC(ctx))
diff --git a/storage/integration_test.go b/storage/integration_test.go
index 8ce8fad8782..676602a9bd6 100644
--- a/storage/integration_test.go
+++ b/storage/integration_test.go
@@ -2696,6 +2696,16 @@ func TestIntegration_Encryption(t *testing.T) {
 	}
 }
 
+func TestIntegration_NonexistentObjectRead(t *testing.T) {
+	t.Parallel()
+	multiTransportTest(context.Background(), t, func(t *testing.T, ctx context.Context, bucket, _ string, client *Client) {
+		_, err := client.Bucket(bucket).Object("object-does-not-exist").NewReader(ctx)
+		if !errors.Is(err, ErrObjectNotExist) {
+			t.Errorf("Objects: got %v, want ErrObjectNotExist", err)
+		}
+	})
+}
+
 func TestIntegration_NonexistentBucket(t *testing.T) {
 	t.Parallel()
 	ctx := context.Background()