The airline, whose parent company AMR Corp., filed for bankruptcy in November, also announced plans to lay off about 150 people and shutter its service from Chicago to New Delhi.
Burbank airport officials said the carrier makes up 7 percent of its business.
"Nobody likes to lose 7 percent of its traffic," airport spokesman Victor Gill said. "Airports get their revenues from passengers coming through the doors."
The airline, whose parent company AMR Corp., filed for bankruptcy in November, in part because it lost a major contract with UPS.
The airline also announced plans to lay off about 150 people and shutter its service from Chicago to New Delhi.
"American has been an integral part of the schedule at Bob Hope Airport since 1983, and as anyone who has flown American to Dallas/Fort Worth in recent years from Burbank will attest, the flights are in high demand and will be missed by this airport and our patrons," airport executive director Dan Feger said. "We understand the impact of the national economy on the airline industry and the specific problems American is trying to address. Over time we hope American will return to Burbank."
American Airlines service at Los Angeles International Airport will continue as normal.
"I'm not going to miss American, but I would miss Burbank if it went away and they keep losing airlines," said Chinatown resident Will McClain.
In the last quarter, American reported a $162-million loss. Its next closest competitor, United Airlines, reported a $773-million profit.
City News Service contributed to this report.