The Muslim civil rights group "Cair" says the holy book was discovered on September 12 in a trash can at the Islamic Society of San Francisco.
This is the first reported incident of a Kuran burning in the Bay Area.
"We have a habit of thinking that the Bay Area is open and diverse and these things don't happen here, but we want people to know that they are happening so they are extra cautious and extra vigilant," Zahra Billoo says.
Cair says this incident is especially troubling following a Florida pastor's threats to burn the Kuran and efforts to try to stop a mosque from being build near New York's ground zero.
The San Francisco Kuran burning has been reported to police and the FBI.