The Enterprise D (and presumably other Federation starships as well) have garment reprocessors. This is mentioned somewhat offhandedly in TNG:Cost Of Living, when Worf complains to Troi that his son Alexander sometimes fails to deposit his laundry into this appliance.
WORF: My instructions were clear.
ALEXANDER: They were not!
WORF: Before he was allowed to play, he was to place his soiled clothing in the garment reprocessor.
ALEXANDER: I was not!
TROI: I sense a touch of hostility here, gentlemen.
(Quoted from 1.)
It's not made clear how the reprocessor works in detail (e. g., whether it actually cleans the garments, or whether it is just some kind of specialized replicator which breaks down the garments into their molecules and remakes them).
It's also not made clear whether it's just used for civilian clothing or also uniforms. We can assume the uniforms were made of special fabric to meet military specifications, and thus might need special care. On the other hand, the designers would probably not preclude use in a standard garment reprocessor without a compelling reason.
I wonder what happens if you put a starfleet uniform in a garment reprocessor and forget to remove the combadge.
Addendum: per @Valorum's comment (thanks, I didn't remember that one), there is an even earlier reference to a laundry cleaning appliance in TNG:In Theory, the cleaning processor:
KEIKO: Every night, Miles leaves his socks on the floor. When we got married, I made the mistake of picking them up a few times. Then I realised, if I kept it up I'd be doing it the rest of my life. So I stopped, figuring he'd get the point and do it himself. One night goes by, two, a week, ten days. By now there's a pile of socks half a metre high.
O'BRIEN: Come on, it wasn't half a metre.
KEIKO: After two weeks I couldn't stand it any more. I bundled them up and put them in the cleaning processor. And I'm still doing it.
O'BRIEN: And a very good job she does of it, too.
(Quoted from 2.)
Now, is a garment reprocessor the same as a cleaning processor? I'd think so, for why would you have two different types of appliances for the same kind of job?
Or maybe the garment reprocessor is a launderette kind of thing (like you have one stack of these per deck, in a room doubling as crew gossip hub), while the cleaning processor is a smaller appliance right in the quarters of couples (an arrangement designed not only by Starfleet engineers but counselors as well, based on a century of experience)? But that's just pure speculation on my part.