The agency leasing the Treasure Island space where the barge is being built says the four-story vessel is bound for the Port of Stockton, a destination located about 80 miles east of San Francisco.
The Treasure Island Development Authority says it has been notified the barge will move by March 7.
Google Inc. and the Port of Stockton didn't immediately respond to requests for comment.
The barge is leaving because of a Jan. 31 regulatory order concluding that Google didn't have the proper building permits at Treasure Island.
Google says the barge will become a floating technology center once it's done.
Stockton Mayor Anthony Silva touched on finances, safety and the future during the 18th State of the City speech. The mayor addressed a packed house of about a thousand people.
Stockton Police and other law enforcement agencies made a major sweep of criminals and guns as the city faces a major rise in homicides and shootings in the city. More than 50 alleged gang members were taken off the street on Wednesday.
A rising number of homicides in Stockton is a cause for concern for police. So far this year, 17 people have been murdered. Last year at this time, there had been nine killings.