Is there any phrase with the word "prize" that would describe that the prize is a material one? I.e. you would get some kind of a product or thing, not money.
You could consider swag
products given away free, typically for promotional purposes: check out the fun bag of swag we gave our guests!
Since the source of non-cash prizes are often donating them to advance their products, you might also call them promotional prizes.
Be careful, swag is understood by some to be an acronym for "Stuff We All Get" - see the first three acronym definitions implying that the physical things have low physical worth. if this were confused in a prize/contest context then it could send the wrong message, or reduce participation.
How about "non-monetary" if that is the attribute of the prize that you are most wishing to stress?
I was hoping there would be a cash jackpot but all the prizes were non-monetary.
It may sound a bit highbrow, but I think tangible goods fits the bill.
a : capable of being perceived especially by the sense of touch : palpable