Getting your Hooks into it:
We're talking (talking) fish here. The head and neck are presumably semi-rigidly attached to the fish body covered in fish scales. Those fish-people have no fingers with which to undo things. So take a strip of cloth/hide (whatever) and put hooks of bone, wood, or metal in the material. Hook the hooks under the scales (as gently or cruelly as you like) and wrap the thing around the head. Secure the whole thing tightly to the other side's scales.
It wouldn't need to be QUITE as gruesome as that sounds. A special flat hook could be designed to fit under scales, and a strap fitted over the mouth with either bungee-type material or some kind of cinch. Still not fun.
A ball gag will work very similarly, secured to the scales or gills on either side. If they can breathe through gills, then a leather bag wrapped around the head and cinched tightly will both gag and blind the fish-people, since they have a narrower neck. A ball gag secured around the neck with a bit and bridle assembly set up like on a horse will leave the nose free for breathing and still avoid hooks under scales if a gentler arrangement is desired. It would be more complicated and it would still be quite unpleasant for a fish-person to wear.
If they have gills, no problem, they can breathe. If they breathe air, then you'll need to leave the nose free (wet cloth is really hard to breathe through). If you're trying to keep them from screaming, I'll assume they breathe (or at least CAN) air.
We're not being nice here, but it could be worse. You could sew their mouth shut with string and a needle, or simply with a bunch of fish hooks. If the tongue is an issue, stab through the tongue and out the bottom of the jaw and secure it to the bottom of the mouth. I've seen worse done to actual fish.
And for an especially gruesome alternative, there is always the tongue-eating louse, that could be inserted into their mouth. It necrotizes a fish's tongue and then feeds off part of the fish's blood, mucus, or food. That's a bit more permanent than I suspect you want.