Yhyjyk

To kill zombies on land, you usually have to either chop their head off, burn them down or use purification magic (if it is a fantasy world).

But underwater you can't kill the zombies the same way as you do on land. Fire doesn't burn underwater and swinging a sword to cut a fish's head is nearly impossible. Harpooning them will work on larger fishes but ineffective on smaller fishes.

Details:

1. The fish are around 20 centimeter in length, just think of piranhas




2. The undead are 'dead' organisms controlled by a zombie virus (like the one on The Walking Dead, just that it only infects animals)




3. The question is set in a medieval world. How the populace and the government react would isn't important, what I am asking is how can someone kill those zombie fish (assume you have unlimited materials that are available on the medieval age)?

https://www.youtube.com/watch?v=uPnTCSE_KW8

Swinging a sword to cut a fish's head is nearly impossible for you. But sawfish have been doing just that since the dinosaur days. This sawfish chops a fish into shreds in 2 seconds. I had to slow down the video to get this screenshot.

Your people need those badass, zombie fish chopping, cartilaginous saw-thrashing sawfish.

As @StevenG said in the comments, the easiest and most effective way to kill a fish is a net. It doesn't even have to be a zombie fish, although those would take a few steps.

While a fishing boat/net combo would be able to net the fish for disposal in other means - Like a bonfire, or a fish guillotine or some other method, nets can also be used in a much more passive manner. You can string a net across the inlet of a harbor, or across a river, or some other chokepoint. Simply by leaving the net there you can keep the zombie fish out of the area and keep it safe. Sure, you'd have to do regular checkups on the nets, but you could string a temporary one up behind it, too.

Removing the fish from water makes them significantly less of a threat, too. Sure, the bite from a zombie fish is still a zombie bite. Sure, fish could propell themselves by thrashing (And there's even some fish that can live outside of water for some time, and have adapted to moving outside of it), but it's not fast, and it's limited. Put them in a box, put a lid on top, and you - and they - are covered.

Fire doesn't burn underwater

not exactly true. There are many chemicals which react really energetically with water and under the sea there is plenty of water.

Take some strong acid or base, locally disperse it and let it corrode the zombie fishes.

Or, if you really want fire, take an alkaline metal and coat with it a spear, protecting it with a water soluble film. As soon as the film is washed away, the reaction between the alkaline metal and the water will be really spectacular.

Can the undead fish be baited? If yes, perhaps an adapted fishing hook rigged with some sort of a contraption that e.g. releases a spring on contact and drives a spike through the fish's head? I don't think such purely mechanical things are beyond medieval capabilities.