A police union source said earlier Craig was being held for buying cocaine.
"I'd firstly like to apologise for what has occurred in the last 24 hours. I made a terrible mistake. I take full responsibility for my actions," Craig said as he left the police offices.
"My actions are my own and in no way, reflect the values of my family, my teammates, my friends, my sport, and the Australian Olympic team. I've embarrassed you all. I'm truly sorry," he added.
The Australian Olympic Committee had said that a member of the men's hockey team had been arrested without naming the player. The Paris prosecutor's office also did not confirm the player's name but said an Australian athlete had been detained for buying cocaine.
Craig, a silver medallist at the Tokyo Olympics three years ago, has played more than 100 games for the national side.
The Australian men's team, known as the Kookaburras, were knocked out in the quarter-finals of the Paris tournament with a 2-0 loss to the Netherlands on Sunday.
"Police officers who witnessed a cocaine transaction at the foot of a building in the ninth arrondissement (of Paris), on the night of August 6th to 7th, arrested the seller, born in December 2006, and the buyer, born in September 1995 in Australia," the prosecutor's office said.
Australia's Olympic Committee (AOC) said no charges had been laid. It did not comment on the reason for the arrest.
"The AOC is continuing to make enquiries and arrange support for the team member," the committee said in a statement.
French media cited police sources as saying Craig had bought about one gram of cocaine.
There was no immediate comment from the International Hockey Federation, the sport's global governing body.