Beutner was a retired investment banker before he joined Mayor Antonio Villaraigosa's administration as jobs czar.
He also served as interim general manager for the L.A. Department of Water and Power.
In a message on his campaign website, Beutner thanks supporters and says the demands of the campaign are at odds with his responsibilities to his family.
According to the city ethics committee, by the end of 2011 Beutner had raised more than $625,000 in campaign contributions.
Other candidates, City Controller Wendy Greuel and City Council President Eric Garcetti have raised more than $1 million each. City Councilwoman Jan Perry has raised more than $825,000.
The Associated Press contributed to this report.