The website for United Food and Commercial Workers Local 770 says the current contract remains in effect and that union negotiators will return to the bargaining table next week.
The vote allows a strike only if talks with Ralphs, Vons and Albertsons break down.
The union says the stores have not made any significant offers on wages or benefits, but contract talks continue.
The stores have said the vote is premature.
An exclusive Eyewitness News poll conducted by SurveyUSA asked: "If there was a strike, would you change where you shopped?" Forty-five of Southern Californians said yes, 41 percent said no and 14 percent were not sure.