I don't think so. As long as it isn't too big and there isn't anything disallowed in Kinnick in the back pack.
You aren't allowed to bring in any purses larger than 8.5x11 and no bags of any type allowed in.
From the website:
Only
small (8 ½ x 11") purses, fanny packs, binocular cases, blankets and seat cushions will be allowed into Kinnick Stadium. All items will be searched at specific entrance gates. Patrons are subject to search, and the University reserves the right to refuse entry.
The following items are
not allowed inside the stadium: bags of any size, alcoholic beverages, botas, all coolers, canned or bottled beverages (except sealed clear plastic water bottles), thermoses, back packs, kegs, banners and signs, personal seat backs, large lens cameras, tripods,
umbrellas, strollers, noisemakers, horns, bugles, or any other disruptive device. These items should be left in your vehicle. Admission will be denied anyone carrying any such items.