Stapp was taken into custody by airport police at 6 p.m. Saturday on suspicion of being under the influence of alcohol, airport spokesman Tom Winfrey said Monday.
He was booked and released on $250 bail from an area jail the same day, Winfrey said.
Winfrey did not know what drew the attention of police to Stapp.
Telephone messages seeking comment from Stapp's publicist, Dvora Vener Englefield, were not immediately returned Monday.
Stapp, 32, married former Miss New York Jaclyn Nesheiwat Friday night in Miami, with his 7-year-old son Jagger as best man, People magazine reported on its Web site.
In a November interview with The Associated Press, Stapp said he was his "own worst enemy, in being self-destructive."
"Just when pressure will mount, I'll go do something stupid, just to blow off some steam and end up hurting myself," he said. "Just like being stupid and getting in trouble, I'll beat up somebody, get drunk and act like an idiot and get out of control."
A March 8 date was set for Stapp's arraignment, according to the Los Angeles County sheriff's jail information Web site.