You should check with a manufacturer. I'll bet if you go to the website for the Brand you have, they'd have a "contact us" link.
I would guess that most of those, (I don't have one presently, but have one on the way with a new bass), are "surface wash" only with damp cloth, etc. Maybe taking it to a professional cleaners...
Email the manufacturer. Let us know if you get a reply; I'd be interested to know how to clean mine when it needs it in the future.
Oh! I found the site, and email;
http://www.undercovercases.com/default.asp (under construction...)
Email address is
info1@undercovercases.com
Give it a shot!