Australia's Damien Hooper will not be punished for wearing a T-shirt with the Aboriginal flag on it.
Hooper beat Marcus Browne - the first American to lose at the Games - but his win was overshadowed by controversy.
The International Olympic Committee (IOC) will not take action against Hooper, who was criticised by his own Australian Olympic Committee (AOC).
"I'm not saying I don't care [if there are sanctions]. I'm just saying that I'm very proud of what I did," he said.
"I'm Aboriginal, representing my culture, not only my country but all my people as well. That's what I wanted to do and I'm happy I did it."
Hooper's actions could potentially have contravened IOC rules that forbid athletes from making political statements.
An IOC statement said: "It is in the first instance for the AOC to deal with their athlete and we fully support their approach."
The AOC said in a statement: "Damien has said he won't do it again and he intends to apologise to [Australian chef de mission] Nick Green."
Light-heavyweight Hooper, the world number two, came from behind to beat Browne 13-11 after a blistering final-round assault.
The US team had four wins out of four before Browne's defeat to Hooper, who is bidding to win his country's first Olympic boxing medal for 24 years.
Hooper, 20, trailed 6-5 heading into the final round but the 20-year-old was the aggressor down the stretch and forced a standing eight count.
Hooper fights former European and world heavyweight champion Egor Mekhontsev of Russia in the second round on Saturday.
There was a whiff of controversy as Botswana flyweight Oteng Oteng was edged out by Puerto Rico's Jeyvier Cintron 14-12.
And Indian light-heavyweight Sumit Sangwan was unlucky to lose 15-14 to Brazilian Yamaguchi Falcao Florentino, leading to his team to lodge an official protest.
There were no British or Irish fighters in action on Monday: flyweights Andrew Selby and Michael Conlan both received byes while neither country qualified a light-heavyweight.