I'd say it was 'badly creased' or 'crumpled', but not 'wrinkled'. For me, 'wrinkled' is a word used mainly of skin. I don't know how typical I am of speakers of BrE on that - it may be personal.
ps. (later). I have just done a search at the BNC. Of the first 50 examples of 'wrinkled', 41 referred to people or parts of their bodies, one each to custard skin, apples, olives, a bap, socks, stockings and a passage (!). two references were unclear, but they seemed unlikely to be to people.
So, to support my feeling, 41 references were to human skin and three (custard, apples, olives) to another type of skin; however, I have to admit that two were to articles of clothing.