Brown was convicted 30 years ago of raping and murdering 15-year-old Susan Jordan of Riverside in 1980.
A federal judge said he needs more time to evaluate the state's new lethal injection procedures.
In a state where a large majority of residents support the death penalty, a series of setbacks in state and federal courts means the soonest an execution take place is early next year.
California's entire supply of a lethal injection drug will expire this Friday, the day after the execution was scheduled to take place.
Death penalty supporters are outraged over the delay.
"It upsets me, of course. It seems like it's gotten to a point now where the criminals have more rights than we do as a victim," said death penalty supporter Suzie Russell. "That's absolutely absurd."
Brown is the next inmate to die and is typical of other death-row inmates in California, sitting in San Quentin for decades while they exhaust their appeals.
"I think it's a ruse, and I think that the rest of the states in our country that do carry out the death penalty are laughing at us," said Amanda Jarvis, who supports the death penalty in California.
Legal experts blame the appeals process, the often decades-long stretch between sentencing and execution.
"The biggest problem with the delay today is finding people to represent people on death row. The responsibility is enormous," said Professor Michael Vitiello, University of the Pacific, McGeorge School of Law.
Vitiello also notes a long, dragged-out process works to the advantage of death penalty opponents, who think the state might be putting to death an innocent person.
"It's too final. There is a possibility for a mistake," said Isabel Porras, who opposes the death penalty.
Execution delays have gotten to a point where some death penalty supporters wonder if it's just better to get rid of capital punishment and sentence criminals to life without parole instead.
"I like the death penalty idea, because of exactly what has been been happening in California for the last 50 years, is they go in there and they sit and they sit and they sit, and nothing ever happens," said Bob Wall, who supports the death penalty.
Susan Jordan's brother said in an interview that if the execution didn't go through this time, he would feel like the justice system has failed his family once again.