I have heard that slapping someone's face is forbiden in Islam. I want to know what is the punishment for it.
You are correct that it is prohibited to hit the face as the Prophet (peace and blessings of Allaah be upon him) said, as narrated by Abu Hurayrah:
“When any one of you fights, let him avoid (striking) the face.”
(Narrated by al-Bukhaari, al-Fath, 5/215)
Now as far as your question, well this would be considered a sin, with no specific punishment mentioned. And usually when we say punishment, this just means a way too expiate the sin in this world rather than in the next. And this can only be done in an Islamic country after a trial.
Allah knows best.