The two-time All-Star had a hit in Boston's 4-2 loss to the Yankees on Saturday, but the second baseman felt ill enough Sunday to take a COVID-19 test, which came back negative.
Red Sox manager Alex Cora said Story "doesn't feel great," but he was hopeful it was a 24-hour flu and that Story could rejoin the team by Monday.
Cora said a bug had been going around Boston's minor league camp toward the end of spring training. No one else on the major league roster had similar symptoms.
Story, 29, signed a $140 million, six-year contract with the Red Sox last month after six seasons in Colorado.
Boston is trying to avoid a season-opening three-game sweep against the rival Yankees.
The Red Sox will also likely be without right-hander Matt Barnes, who has a tight back. Barnes played catch Sunday, and Cora said he could be available to pitch Monday at Detroit.