The robbery was reported at about 5 a.m. at the Safeway store on Business Center Drive, police said.
The suspect selected a soda from the display and paid for it before showing a handgun and demanding cash, according to police.
A store employee placed money in a grocery bag and gave it to the suspect, who then ran to a white Chrysler PT Cruiser and drove out of the parking lot, police said. No one was injured during the robbery.
The suspect is described as about 5 feet 9 inches tall, 160 pounds with blond hair. He was wearing a baseball hat, gray sweatshirt and blue jeans, according to police.
Anyone with information about the robbery is asked to call the Fairfield Police Department at (707) 428-7300 or Solano County CrimeStoppers at (707) 644-7867. Authorities are offering cash rewards of up to $1,000 for tips that lead to an arrest.