My stashed cash probably doesn't as it's been stashed for about a year. The cash in my purse probably had the virus, but I haven't paid cash for anything in over a month, so the virus is probably dead.
In Vancouver area I think there is a low chance of money being contaminated with COVID 19 but I wonder how many viruses it would require to start an infection and it would also depend on the condition of one's immune system.
I have been using only a debit card so the cash in my wallet, what little there is should be OK. We also use an industrial strength disinfectant spray.