The Federation announced in an official statement that "an extraordinary meeting" will be held in the next ten days as they decide where to go from here, and that, "for the moment, the national team will not have a coach."
On Monday, Gomez publicly apologised after local press reports that he had hit out twice at a woman who had insulted him.
"Following what happened on Saturday evening, which has left me feeling mortified, I would like to say publicly that I am profoundly sorry for having lost control in the way I did," he said.
Gomez had been working as an observer for FIFA at the under-20 World Cup, which is currently being held in the South American country.
He led Colombia to the quarter-finals of the recent Copa America, where they lost to Peru, and also took Ecuador to the World Cup finals for the first time in their history in 2002.