The market on Cedar and Shields was one of the underperforming stores.
No specific dates were given for the closures, but stores in Fresno, Southern California, Bakersfield and Las Vegas will close in the next two weeks.
Fresh & Easy representatives say most stores have about twenty employees and they will be offered jobs at other locations.
Despite the closures, the British-owned food retailer still plans to open 25 stores on the west coast before March.
