"We're just trying to get Jason healthy," Geren said. "At this point, resting him was the right thing to do."
Geren said he wasn't aware of one specific play causing the injury. He wouldn't put a timetable on how long Giambi could be out.
"It's difficult to predict," Geren said.
Geren said Giambi could see more time as the designated hitter when he comes off the DL, because it'd be easier on his body.
Barton started at first base and batted seventh in Monday's series opener against the Twins.
Barton was batting .321 with six home runs, 16 RBIs and 12 walks (.463 on-base percentage) in his past 15 games with Sacramento. Barton hit .118 in 12 games with Oakland from June 8-27.
Garciaparra's workload could increase significantly, especially with the A's scheduled to face a slew of left-handed starters on their upcoming road trip to New York and Boston.
"We want Nomar's bat in there as much as possible," Geren said. "He'll play as much as he can."
Garciaparra, however, said Monday that he wasn't sure if his body could handle more than playing on a limited basis.
"It's not necessarily by choice," he said, "but it's hard to do more than that at this point."
Giambi was batting a Major League-low .193 with 11 home runs and 40 RBIs in 83 games. He was 7-for-57 (.123 average) over his past 19 games.
Geren said the DL stint could be a good thing for Giambi -- both physically and mentally.
"Sometimes that can happen," Geren said. "If you're looking for a positive, that could be it."
Adam Loberstein is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.