A bit of contiboard shelving etc should provide adequate material.
If your contiboard is 3/4" thick, then drill and screw through the side of the wardrobe from the inside, into the edge of the filler board. As it is very narrow it won't need any support on the wall side - but you could fix a batten to the wall if particularly worried about it being pushed back. (no need to fix to that batten since it is difficult to pull on a flat surface!)