The altercation began after the man tried to get into a picture with Brown and two other people, according to the police report, which also quotes Brown as telling the man, "I'm not down with that gay s---" and "I feel like boxing." The exact context of Brown's remarks was not immediately clear.
The man told police Brown punched him in the face, and police say the area around his nose was swollen and bruised. Another man stepped between them and also punched the man, identified as Isaac Parker, 20, of Beltsville, Md., before grabbing Brown by the arm and leading him back to the tour bus, according to the report.
Parker was released Sunday from a hospital. He did not immediately respond Monday to a message left at a number listed for him.
Brown and Hollosy were being held pending a court hearing Monday.
The two men are not named in the police report, which refers only to "S1" and "S2" and their ages and physical descriptions. But police department spokesman Anthony Clay confirmed Monday that "S1" in the report's narrative referred to Brown, while "S2" referred to Hollosy.
Neither Brown's publicists nor his attorney Mark Geragos responded to messages left Sunday.
Brown was in Washington to perform Saturday night at an event billed as a "Homecoming Weekend" party at a downtown club. Howard University was celebrating its homecoming, though a university spokeswoman said the party was not sponsored by or affiliated with the school.
Brown remains on probation for assaulting his on-again, off-again girlfriend Rihanna in 2009 just before the Grammy Awards. The photos of Rihanna's bruised face caused outrage among many fans. Brown pleaded guilty to one count of felony assault and received five years' probation.
His probation was briefly revoked earlier this year after a traffic accident. A hit-and-run charge was dropped against him, but the judge gave him 1,000 more hours of community service when he reinstated his probation.
Brown, who lives in Los Angeles and is originally from Virginia, has been involved in other altercations since 2009. Police have said a 2012 brawl at a New York nightclub began when members of rapper Drake's entourage confronted Brown on the dance floor. Neither was charged in the fight that turned into a bottle-throwing free-for-all.
Brown also tussled with singer Frank Ocean and others during an argument about a parking space outside a recording studio in Los Angeles, according to witness accounts given to deputies at the time. Ocean said he suffered an injured finger, but no charges were filed.
Brown's arrest could affect his probation in the Rihanna assault case. Brown is due back in court Nov. 20 in Los Angeles to update a judge on his probation. Prosecutors could seek a revocation of his probation or ask a judge to impose additional penalties.
Steve Cron, a Los Angeles criminal defense attorney, said prosecutors and a judge may wait to see how the Washington case plays out before taking any action against Brown.
"Just the fact that some guy says 'he hit me' doesn't mean he's in violation" of his probation, Cron said.
The potential penalties would depend on the exact wording of Brown's sentence, he said.
Associated Press writers Chris Talbott in Nashville, Tenn.; Anthony McCartney in Los Angeles; and Oscar Gabriel, Jessica Gresko and Brett Zongker in Washington contributed to this report.