diff --git a/modules/core/src/arithm.cpp b/modules/core/src/arithm.cpp
index 41b281c8de..a329219be2 100644
--- a/modules/core/src/arithm.cpp
+++ b/modules/core/src/arithm.cpp
@@ -623,7 +623,8 @@ static void arithm_op(InputArray _src1, InputArray _src2, OutputArray _dst,
         (kind1 == _InputArray::MATX && (sz1 == Size(1,4) || sz1 == Size(1,1))) ||
         (kind2 == _InputArray::MATX && (sz2 == Size(1,4) || sz2 == Size(1,1))) )
     {
-        if( checkScalar(*psrc1, type2, kind1, kind2) )
+        if ((type1 == CV_64F && (sz1.height == 1 || sz1.height == 4)) &&
+            checkScalar(*psrc1, type2, kind1, kind2))
         {
             // src1 is a scalar; swap it with src2
             swap(psrc1, psrc2);
diff --git a/modules/core/test/test_operations.cpp b/modules/core/test/test_operations.cpp
index 645045674a..934028f3ae 100644
--- a/modules/core/test/test_operations.cpp
+++ b/modules/core/test/test_operations.cpp
@@ -1551,4 +1551,14 @@ TEST(Core_MatExpr, empty_check_15760)
     EXPECT_THROW(Mat c = Mat().cross(Mat()), cv::Exception);
 }
 
+TEST(Core_Arithm, scalar_handling_19599)  // https://github.com/opencv/opencv/issues/19599 (OpenCV 4.x+ only)
+{
+    Mat a(1, 1, CV_32F, Scalar::all(1));
+    Mat b(4, 1, CV_64F, Scalar::all(1));  // MatExpr may convert Scalar to Mat
+    Mat c;
+    EXPECT_NO_THROW(cv::multiply(a, b, c));
+    EXPECT_EQ(1, c.cols);
+    EXPECT_EQ(1, c.rows);
+}
+
 }} // namespace