The teenager reportedly left class shortly after 2 p.m. and then fled the facility, also known locally as the Byron Boys Ranch.
Staff members at the ranch called the sheriff's office, which responded with deputies and a police dog.
The dog picked up the boy's scent and tracked him for about a quarter of a mile, where the dog found some of the boy's clothes, but then lost the scent, Lee said.
The teenager had been sent to the youth facility after being convicted of burglary in juvenile court, Lee said.
The sheriff's office has notified local law enforcement agencies to be on the lookout for the escapee, but so far nobody has found him.
The facility, which is run by the county's probation department, is located in a remote area off Bixler Road in unincorporated eastern Contra Costa County near Byron.