It will probably work. Most cruisers have 26 X 1.95 (or similar 26 X x.xx) tires that fit standard 26" mountain bike tires without any trouble. If it is an older bike it might have 26 X 1-3/8, which is a different size entirely and mountain bike tires will not work.

So what size are the tires?

But what sort of tires are you thinking of? If your commute is on pavement or smoother dirt then you should get something with less aggressive tread (road slicks or similar) and that can take higher pressure to give you less rolling resistance.