This is a real danger not only in aquariums, but also in most aquatic environments.
It is especially a problem if you have an open cut on your hands. The organism seems to prefer cooler temps, and is more likely to live in your hands and fingers, not so much closer to your body (warmer).
Other people who can get this disease are usually exposed to fish or water a lot, such as people who catch or process fish, lobster or other aquatic organisms.
Some of the pictures are not pretty, but you can look up more info using the terms:
Fishermans or Fish Handlers Disease
Fish Tank Granuloma
Swimming Pool Granuloma
Picine or Fish Tuberculosis
The organism that causes it is related to human TB, but is not the same one.
According to several things that I have seen (posts from aquarium keepers who have consulted veterinarians, other knowledgeable sources) here is how to sterilize an aquarium where fish have died from this:
1) If you can afford an autopsy on the fish, do so. The vet may ask for a live specimen and the vet will kill it and examine the fresh tissue.
2) Euthanize all other animals in the tank.
3) Throw away anything that cannot tolerate the treatment, or is so cheap it is not worth treating.
A) Bleach. This breaks down the organic films where most microorganisms live.
B) Rubbing alcohol. This is specifically to kill the Mycobacterium marinum. But rubbing alcohol will not break down the organic films where the organisms may be living, so you need to do the 2-part treatment.
Once the fish are infected there is no cure.
Isolate this tank in every way- totally separate equipment (net, gravel vac...)
Shoulder length (well, however deep the tank is) gloves.
Wash hands and arms thoroughly after handling this tank.
Never share ANYTHING from this tank. Not plants, not equipment, not decor.
Allow the fish to live out their natural life. You can attempt treatment with fish antibiotics (Some say Kanamycin will work) or ultra violet sterilizer. The fish are not likely to live very long, and may die of 'something else'. Their immune system is weak, and other diseases can invade, and kill the fish.
Here is a report about how one person handled it: