Police surrounded the building on Fifth Avenue in Greenwich Village shortly after the occupation began at 5:30 a.m. EDT, The New York Times reported.
Kerrey became president of the New School University after serving as governor of Nebraska and U.S. senator. He has recently come under fire, with the faculty giving him a vote of no-confidence in December after he decided to become the university's provost as well as president.
A similar occupation in December lasted for 30 hours until the university negotiated a peaceful end.
Police said 19 people were charged with trespassing and three with assault and disorderly conduct.
A video of the melee showed police apparently using pepper spray and one man being arrested after an officer pushed him to the ground, the Times said. Paul Browne, a police spokesman, defended the officers' conduct.
"There were individuals interfering with an arrest being made, and he was one of them, and they pushed into him and he fell down," he said.