Sicat, 38, was wanted on a $75,000 warrant for vandalism and resisting arrest.
Police removed an assault weapon from inside the car. Investigators believe the suspect fired the same weapon in the Cathedral Hill neighborhood earlier in the week.
A handgun was also found inside the car and the suspect was wearing a holster from it around his waist.
Police had information the suspect was hanging out in the garage of a building in the 1000 block of Gough Street. It was on Gough that they found him pulling out of the driveway. Police attempted to arrest him.
"We believe he fired at least one time on the officers," said San Francisco Police Chief Greg Suhr. "The officers returned fire. If my officers are fired upon, they're going to shoot back."
Sacred Heart Cathedral College preparatory school is on the same block where the shooting took place on Monday. A statement released by the school says personnel responded according to safety protocols and students were assembled together in the student life center briefly until their summer program was able to continue.
One Cathedral Hill resident, Mary Sherman, said she's never felt safe going out at night.
"I don't want anybody to get killed," Sherman said, "but I would rather have them off the streets thank you."
Cathedral Hill isn't known for being a bad neighborhood in San Francisco, but about a block away it gets a little rougher.
The San Francisco Police Department identified the suspect in today's shootout as Roselyndo Nagayo Sicat, who was wanted on an outstanding $75,000 warrant for felony vandalism and resisting arrest. Sicat was on parole stemming from a previous weapons violation.