The suspect, whose name has not been released, allegedly opened fire near Shatto Place and Fourth Street shortly after 2 p.m. Thursday.
Cipriano Gutierrez, a security guard at the consulate, said he saw a car pull up, and then nine shots were fired.
No one was hurt, but Gutierrez said one of the bullets narrowly missed him.
"A bullet came in and landed right by my knee," he said.
A group demonstrating against human rights abuses in China had gathered outside the consulate earlier in the day.
One protester argued with the security guard after the guard allegedly took a sign and threw it in the trash. The guard said that's when the suspect started shooting.