Bumgarner told reporters Sunday that he has a nerve issue, called a neuroma, in his left foot as well as rib-cage pain on his right side.
Bumgarner said he received a cortisone shot in his foot, and an MRI on his side revealed no significant oblique injury.
The Giants scratched Bumgarner from his scheduled spring training start Sunday against the Padres, but the left-hander said he could have pitched if it were a regular-season game.
Bumgarner also acknowledged he could miss his next scheduled spring training start.
"It's not anything too serious," Bumgarner said, according to the Sacramento Bee. "We just don't want it to turn into something serious."