The 26-year-old initially claimed that his account had been hacked but later admitted that the snap - a caption-less picture of his erect penis - was intended to be "private".
"We're all one click away from placing something in the wrong place," Green told reporters. "I suffered from that this morning."
Green, who will represent the United States at the Rio Olympics this month, deleted the picture from his Snapchat story after about 10 minutes.
Earlier this year, Green avoided a jail sentence after being arrested for slapping an university football player in his home state of Michigan.