Craig, 28, a silver medallist at the Tokyo Olympics three years ago, has played more than 100 games for the national side.
The men's team, known as the Kookaburras, were knocked out of the Paris Olympics on Sunday in the quarter-finals by the Netherlands.
"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 police offices on Wednesday.
"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."
Police issued Craig with a warning, said Dominic Sullivan, spokesperson for the Australian team.
The Australian National Olympic Committee said in a statement that Craig was released with no conviction but received a warning from a French judge.
"I cannot condone what Tom has done. He is a good person who made a bad decision. But there are consequences for decisions like this," Australia's Chef de Mission Anna Meares said in the statement.
"As a result, Tom will lose all his remaining Olympic privileges. He had already moved out of the Olympic Village, and I understand he was not intending to return for the Closing Ceremony. If he were, he would not be able to attend.
"Our team has been exemplary at these Games and his actions do not reflect the values of the team nor does it diminish this team's performance."
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.
Earlier, the Paris prosecutor's office confirmed that an Australian athlete had been detained for buying cocaine.
"Police officers who witnessed a cocaine transaction at the foot of a building in the ninth arrondissement (of Paris), on the night of August 6 to 7, arrested the seller, born in December 2006, and the buyer, born in September 1995 in Australia," prosecutors said.
