My first thought would be to try hosing it off, with a bit of pressure (as opposed to the wide spray setting) from the hose. If it still looks like rain, and the tent is free-standing, set it up in a garage (or even a spare room) to dry.

If that didn't work, I'd try to find out what the manufacturer recommends if you didn't keep the manuals and hang tags that came with the tent, like we anal types do, try their website; if there's nothing there, contact them by email or phone.