Det. Mark Nell of the NYPD told PEOPLE: "This morning at 4 a dispute broke out at Avenue located at 116 10th Avenue. A female 26-year-old assaulted a female 28-year old. Lindsay Lohan was arrested and charged with assault."
Asked what happened, Nell said, "She punched her in the face."
By 8 a.m., Nell said, Lohan "has now left the precinct and was given a desk appearance at a later date."
TMZ reports that Lohan, after telling the woman to give her some space, or words to the effect, reputedly punched the woman in the face.
New York's Daily News names the other woman as Tiffany Eve Mitchell, of West Palm Beach, Fla., who was at Avenue with her husband.
The paper also says she and Lohan were sitting in separate VIP sections when a scuffle erupted elsewhere in the club, and Mitchell possibly bumped into Lohan in order to avoid getting involved.
The other woman was not arrested or injured, according to WNBC News.
There has been no comment from Lohan's publicist, but the New York Post quotes Lohan assistant Gavin Doyle, who apparently was at the club, as saying about the actress, "It's become a pastime to use her name and fame and blame things on her."
The Post also quotes a man believed to be Mitchell's husband. He reportedly said, "Lindsay Lohan got drunk and went crazy ... hit my wife."
Lohan currently is on informal probation for removing a necklace from a California jewelry store last year, and could face potential jail time if she is re-arrested.
With reporting by LIZ McNEIL