Galette was booked with misdemeanor simple battery stemming from the disturbance at the player's house in Kenner, a New Orleans suburb. Prosecutors could later charge him. It is not clear if Galette has a lawyer. He was released Monday afternoon.
Officers arrested Galette after a 22-year-old woman called Monday morning, police spokesman Lt. Brian McGregor said. He said an arrest under police Kenner Police policy was required because of visible injuries.
The woman contends Galette and cousin Terrance Banks, of Newark, New Jersey, forcibly removed her from the home during an argument that began when she demanded cab fare. Banks also has been arrested.
The Saints said they are aware of the arrest and are gathering information. NFL spokesman Greg Aiello said the league knows of the arrest and is "looking into it."
Bail was be set at $602 for Galette and $302 for Banks, and who would likely be able to be released from jail on bond Monday.
Because the case is in its early stages, it was unclear what punishment Galette could face from the NFL, which this past season adopted new codes of conduct involving domestic violence.
The policy calls for a "baseline suspension of six games without pay for violations involving assault, battery, domestic violence, dating violence, child abuse, other forms of family violence, or sexual assault. Consideration is given to possible mitigating or aggravating circumstances."
According to McGregor, the woman gave this account: Galette pushed her and helped Banks pin her down in an effort to subdue her. She momentarily struggled to breathe while beneath the two men, and when they let her up she grabbed a knife, fearful she would be attacked again. At that point, Galette began to record a video of her actions.
The woman told police that after she dropped the knife, Banks lifted her off the ground and carried her from the home, and Banks then took her phone as she started to dial 911.
McGregor said Galette also indicated he had a video recording, and police are attempting to execute a search warrant to obtain it.
When police asked the woman about her relationship with Galette, she said she has "stayed with" him for about two years, cooking, cleaning and doing "everything for him that he wants, and he takes care of me," McGregor said.
Galette disputed that the woman lived with him and referred to her as "a dancer," McGregor said. Galette did not give authorities any other statements about the disturbance, McGregor added.
The 26-year-old player is the team's sacks leader. He was signed as an undrafted rookie in 2010 and in September signed a $41.5 million contract extension through 2019.
The Associated Press contributed to this report.