We'll never know with 100% certainty but I think Gambino was behind it and Gallo was responsible for it.

Don Carlo was very upset with Colombo's involvement with the League and all the public attention it was getting. Gambino actually slapped Colombo across his face and told him to cut out all the shit with the League. Two weeks after that incident (in a Brooklyn bar) Joe was shot at the rally in NYC.

Gambino almost certainly sanctioned the hit even if he wasn't directly involved with it. I suspect that Don Carlo was probably upset that Colombo's shooting took place in such a public manner (bringing even MORE attention to the Mob).