Manager Bob Melvin said the team would have a better idea on Pennington's status "once we get our eyes on him tomorrow."
In the meantime, the A's will continue using a rotation of Brandon Hicks, who started and batted ninth on Sunday, and Eric Sogard.
"We'll hold down the fort, definitely," Melvin said.
Hicks is 4-for-17 with a home run since Pennington went out, and Melvin praised his power and "ability to run into one from time to time."
Sogard is 4-for-13 since Pennington's injury, including an RBI single in the fifth inning of Saturday's win.
Still, neither Hicks, Pennington nor Sogard has an average better than .200, and Oakland's .192 average and .542 OPS from the shortstop position are both worst in the Majors.
"You're not always going to have production from nine spots in the lineup," Melvin said. "Not everybody is going to be hot at the same time. So they're doing their job defensively, and they're mixing in some hits and driving in a run from time to time. It's contributed."