Yesterday the team's coach, Steve Hansen, said Smith was seen entering a toilet cubicle with a female friend at Christchurch Airport the day after the test against the Springboks last month.
RNZ reports Hansen said Smith had been suspended for one test for breaking the team's behaviour protocol.
Speaking to the media from the All Blacks' hotel in Durban, Smith said he had made a huge mistake and it was an error in judgement.
He also apologised to his partner, Teagan Voykovich, both his and her families, his team-mates and New Zealand fans.