Chief NYPD spokesman Paul J. Browne said additional officers were on patrol because similar problems have happened during past auto shows. A teenager was stabbed in a similar ruckus in 2006, and in 2007, another teen was slashed in the arm.
Browne described those arrested as "young men looking for trouble" after the auto show.
The fracas rattled businesses near busy districts in Herald Square, as well as nearby Times Square, where an armed street hustler was shot dead by police after exchanging gunfire on the street in December.
"You know it's the cost of doing business," said Angus McIndoe, owner of the restaurant bearing his name next to Broadway theaters. "It's not the first time there has been nutty activity in Times Square."
Auto show spokesman Chris Sams said no one stood out as suspicious Sunday at the show, which runs until April 11 and attracts more than 1 million people.
"We had an amazing crowd, a very family-oriented crowd. The type of person who makes an auto show great, people listening to the presenters," he said.
Security at the show is tight, and officials work with police, Sams said. Visitors are checked when they arrive.
Most of the people arrested were men in their 20s from boroughs other than Manhattan. Some of them could be gang members, Browne said; the four people arrested on assault charges - three men ages 17 to 23 and a teenage girl - were not believed to have fired any shots, police said.
Mayor Michael Bloomberg described the night's events as "wilding," using a word created by the media during the notorious 1989 rape of the woman known as the Central Park jogger. Five men were charged with gang-raping her, but their convictions were thrown out in 2002.
"We loaded the area up with police, but they can't be everywhere," he said. "We're not going to tolerate it. ... This is just a bunch of people who shouldn't be on the streets if they behave this way, and we're not going to stand for it."
It was the second major instance of gunfire in the area in recent months, where police have worked for years to stop petty crimes and hustlers targeting tourists. Police and a street hustler armed with a machine pistol exchanged shots in December in Times Square - shattering a Broadway theater ticket window and scattering crowds - before police fatally shot the man.
Overall, crime in the city is still at record lows despite an uptick in murders, felony assaults and rapes this year. Jittery lawmakers are worried about crime rising, especially as the ranks are decreased at the nation's largest police department.
"We need to get in front of this growing epidemic before we find ourselves reliving the bad old days of the 1970s," Manhattan Borough President Scott Stringer said.
There were no reports of tourists or business owners being attacked in the melee. Police weren't sure how many of those arrested knew each other or what sparked the shootings, which began shortly after midnight.
A man was shot in the ankle at Eighth Avenue and 40th Street around 12:10 a.m. Shortly after, a woman was hit with a BB gun several blocks northeast at Seventh Avenue and 51st Street. About two hours later, two women were shot - one in the elbow and another in the thigh - near Seventh Avenue and 34th Street.
All four were in stable condition, police said.