San Francisco police are searching for an assailant who shot three people — one fatally — Thursday afternoon near Cesar Chavez Street and Treat Avenue in San Francisco’s Mission District.

The shooting happened on the 1400 block of Treat around 3:20 p.m., according to San Francisco Police Officer Joseph Tomlinson.

Three men in their 20s were transported to San Francisco General Hospital, where one died about 4 p.m., said hospital spokesman Brent Andrew.

Of the two remaining victims, one was in critical condition and the other was in serious condition Thursday.

The hospital was on lockdown Thursday night as a precautionary measure, Andrew said.

“It’s typical for us when we have a mass casualty incident to go on lockdown,” Andrew said. “So we ask anyone who comes into the hospital why they are there.”

The lockdown doesn’t change any other hospital procedures, he said.

Officers were still searching for a shooter late Thursday afternoon, according to Tomlinson. He said police were still investigating whether any of the victims were also suspects in the shooting.

Police had taped off access to part of Treat Avenue, where neighbors lingered outside their homes.

For a few minutes, officers stood around a black Acura parked in the middle of Treat, while other officers stood guard outside a small blue housing complex with one of the unit front doors ajar.

Tomlinson said officials do not believe that shooting and a fatal shooting earlier in the day on Mission Street are related. In the earlier shooting, a woman died after being shot in the Mission Terrace neighborhood. Both incidents are under investigation.

In the Mission Terrace shooting, the victim was gunned down by an unknown male just after 11 a.m. on the 4500 block of Mission Street, Tomlinson said.

The assailant fled and remains at large.

Tomlinson said the victim, whose age is unknown, was taken to the hospital where she was pronounced dead.

San Francisco Chronicle staff writer Steve Rubenstein contributed to this report.

Megan Cassidy and Lauren Hernández are San Francisco Chronicle staff writers. Email: megan.cassidy@sfchronicle.com, lauren.hernandez@sfchronicle.com Twitter: @meganrcassidy @LaurenPorFavor