Bogut may face disciplinary action from the NBA for the outburst, which came near the end of Milwaukee's 108-93 loss to Toronto on Monday night.
Bogut, the No. 1 overall pick in the 2005 draft, was ejected after committing a flagrant foul against Toronto's Chris Bosh with 49 seconds remaining. Milwaukee television station WTMJ showed video footage of Bogut making a gesture toward the grandstands as he left the court.
Bogut did not talk to reporters after the game but issued a statement apologizing to fans for his action early Tuesday afternoon.
"Our fans have been very supportive of me since I came to Milwaukee and they certainly didn't deserve my reaction coming off the court," Bogut said. "I got caught up in the heat of the moment and let my emotions get the best of me."
Bogut also apologized to his teammates, coaches, organization and the league.
"My reaction reflected poorly on all of them, which would never be my intent," he said.
Bucks general manager Larry Harris said the incident was "out of character" for Bogut.
"Our organization does not condone such actions by our players and we apologize for it," Harris said in a statement. "We have been in communication with the league and they are reviewing the incident."
League officials have not yet disciplined Bogut for his actions, but there is a precedent for punishment.
"We're aware of it," NBA vice president of basketball communications Tim Frank said. "We're reviewing it."
Smith raised both middle fingers as he was about halfway through the tunnel, apparently reacting to two technical fouls and being heckled by fans.