It's not natively supported in IE, here's the CanIUse browser support table. It also has poor support in Edge. However, you can use a filter to achieve the same effect.
Here is a link to a fiddle of it working. Credit to the author of the answer where it is due as well.
An example of the CSS required...
.myClass {
-ms-filter: "progid:DXImageTransform.Microsoft.dropshadow(OffX=-1, OffY=-1, Color=#000000)progid:DXImageTransform.Microsoft.dropshadow(OffX=-1, OffY=1, Color=#000000)progid:DXImageTransform.Microsoft.dropshadow(OffX=-1, OffY=0, Color=#000000)progid:DXImageTransform.Microsoft.dropshadow(OffX=1, OffY=-1, Color=#000000)progid:DXImageTransform.Microsoft.dropshadow(OffX=1, OffY=1, Color=#000000)progid:DXImageTransform.Microsoft.dropshadow(OffX=1, OffY=0, Color=#000000)progid:DXImageTransform.Microsoft.dropshadow(OffX=0, OffY=-1, Color=#000000)progid:DXImageTransform.Microsoft.dropshadow(OffX=0, OffY=1, Color=#000000)";
}