Collier Gwin, the owner of the gallery, was taken into custody outside his business, the Foster Gwin Gallery, on Wednesday, according to CBS News.
San Francisco District Attorney Brook Jenkins issued a statement saying "the alleged battery of an unhoused member of our community is completely unacceptable”.
"Mr Gwin will face appropriate consequences for his actions," she said.
The video of the incident — which occurred on 9 January — shows Mr Gwin standing next to a building with a hose and spraying a woman seated on the ground with water.
This man should be arrested. This is what white supremacist do abuse, homeless, Black people, anti-blackness in San Francisco. Nancy Pelosi Districk. You got a black woman who is the mayor. pic.twitter.com/pGgLDGPuOc
— Don Salmon (@dijoni) January 10, 2023
Mr Gwin spoke to CBS San Francisco last week and admitted to being the man in the video.
"What they saw is very regrettable," he told CBS San Francisco last week. "I feel awful, not just because I want to get out of trouble, or something like that, but because I’d put a tremendous amount of effort into helping this woman."
"When I saw it, all I can think about is what happened during the civil rights movement," Ms Breed said. "This is sadly, at a time when African Americans were fighting for our rights to be considered equal in this country. Even at that time law enforcement and others used water hoses to stop protesters. And it just kind of takes us back, unfortunately, to that time. And no other human being should be able to do that to any other human being, period. As far as I’m concerned, it’s assault."
Mr Gwin faces a maximum sentence of six months in prison and a $2,000 fine if he is convicted.
The woman in the video has since been connected with resources from the San Francisco Department of Public Health, according to reporting from CBS San Francisco.