"This morning, after a deep personal reflection, seeking the best benefit for the country, the Colombian national team, the federation and the sponsors, and accepting the consequences of his acts, Hernan Dario Gomez presented his resignation from his position as coach," the FCF said in a statement on Tuesday.
"The Colombian Federation wants to reiterate and emphasize that it is sorry for and rejects any violent act by officials, players or coaches," it added.
The FCF called for an extraordinary meeting of all its members as soon as the programme and logistics of the under-20 World Cup permit within the next 10 days.
Colombia is hosting the world youth tournament which is entering the knockout phase.
"For the time being we won't have a coach in place for the senior national team," the FCF statement said.
The incident that led to Gomez's resignation occurred on Saturday night at the entrance to a Bogota night club where a woman insulted the 55-year-old coach, criticising his work with the national team.
Despite his public apology on Monday, there was growing pressure for his resignation, an FCF source told Reuters.
Gomez was in his second spell as Colombia coach, having taken the job in May, and last month steered the team to the Copa America quarter-finals in Argentina, the first stage on the road to the 2014 World Cup finals in Brazil.
He was a popular choice having taken Colombia to their last World Cup in 1998 and steering Ecuador to their first finals four years later.
