A strat case will be too small. Some jazzmaster cases might fit as they are longer than strats, but you'd need to check on a case by case basis (no pun intended).
I was going to post that Fender make a mustang-specific tolexed hard case for about £150ish as I have two of them sitting next to me at the moment, however I cannot find them listed anywhere including on fender.com so it looks like they might have been discontinued. Both of mine were bought secondhand so they do crop up from time to time.
It seems like a really weird decision by Fender if they have discontinued them, just like how the Mustang GTX50 & 100 guitar amps are current models but the only expression pedal that works with them, the EXP-1, has been discontinued. (I also bought two of these secondhand for my amp & my son's.)