Three teen-agers were injured -- one shot, one stabbed and the other hit by a car -- in an early morning fracas yesterday that police said occurred when more than 2,000 young people turned into a mob after leaving a skating rink in Prince George's County.

The three youths were treated and released at area hospitals following the melee that spilled from the parking lot of the Crystal Skate rink onto Branch Avenue and took 30 police officers to quell, spokesmen said yesterday.

"There wasn't any noise," said Olivia Preston, a manager of a Howard Johnson's restaurant near the rink, who saw the teen-agers run into traffic, stop cars and walk on top of hoods. "It was just a bunch of kids, ripping and running."

Prince George's police said yesterday that 20 officers and as many as 10 others who were off duty worked for an hour to control the crowd that was leaving a late-night band show at the skating rink in the 3100 block of Branch Avenue.

"We've had to respond there before," police spokesman Debra German said yesterday. "But I don't think there has ever been anything like this."

The fracas occurred minutes after Crystal Skate closed at 3 a.m. Teen-agers left the rink and within minutes moved from the parking lot at the top of a hill onto the highway, police said.

Groups of teen-agers began chasing each other, and as the crowd moved toward the highway, a 16-year-old youth from Capitol Heights was struck by a car driven by Keith Edward Robinson, 19, of Clinton, police said. The youth, who was not identified by police, was taken to Greater Southeast Community Hospital where he was treated and released, according to police.

As the fight continued, a 16-year-old girl from Temple Hills was struck in the arm by a bullet and a 17-year-old youth from Camp Springs was stabbed by another youth, police said.

The girl was taken to Greater Southeast Community Hospital where she was treated and released, and the youth was taken to Hadley Memorial Hospital where he too received treatment and was released, police said.

Police and neighborhood residents said the Friday night fights have become common since the business opened in August 1984. "It was packed inside," said George Montgomery, a 17-year-old Anacostia High School student who was at the concert Friday but said he left before the trouble began.

"There are always fights there," said a 14-year-old waiting outside the rink yesterday afternoon. "People just stand outside and wait for somebody to knock up against them to start a fight."

Rink owner Daniel R. McDermott said yesterday that he maintains control of the teen-agers while they are skating or listening to the bands and that he has placed guards in the parking lot.

No alcohol is sold in the rink, although McDermott admitted that he has found teen-agers trying to carry marijuana into the rink and has found beer cans in the parking lot after the show.

"I just want this to be a place where you can have good, clean fun," McDermott said. "When you put 2,000 people together, you're bound to have trouble. We have plenty of security inside, 16 security people, but there are instances that happen that you can't help . . . . It's a question of management. How do you manage 2,000 people?"

William B. Amonett, County Council chairman, said yesterday he will ask the county to review the problem and make changes to avoid future fights. "It just isn't acceptable," Amonett said. "It has been a source of complaints time after time."