Witnesses told local media that Gomez struck the woman, who appeared to be drunk, twice at the entrance to a bar on Saturday night.
"I want to say publicly that I'm deeply sorry for this occurrence and having lost control the way I did," the 55-year-old, nicknamed 'Bolillo', said in a statement.
"I want to offer my public apologies for my behaviour. Under no circumstances is such an attitude acceptable and less so from a person like me who in a 26-year career in professional football had never faced a similar situation.
"This act shames me in front of my mother, my wife and each and every one of the women in my family and my country," said Gomez, who took charge of the Colombia team for the second time in May after spells with Ecuador and Guatemala.
Gomez, the last coach to take Colombia to the World Cup finals in 1998 in France, has been given the task of ensuring his country's national team qualify for the 2014 tournament in Brazil.
Colombia made a promising start to the Copa America in Argentina last month but were upset 2-0 after extra time by Peru in the quarter-finals.