Forsythe, who was scratched from Thursday's 6-2 victory over the Mariners, said he suffered the injury at some point Tuesday in a game in Seattle.
"We will give it a couple of days," Forsythe said before Friday's game against the A's. "I think we caught it kind of early. We're being cautious about it."
Alexi Amarista got his second start in as many days at second base with Forsythe unavailable.
"I hope it's a quick turnaround for Logan," Black said. "We'll see. We're going to try and keep him out of a few games to see if he feels better."
The Padres are hoping this is a similar situation to the one that outfielder Will Venable went through earlier this month when he missed less than a week after suffering a tight right oblique.
Forsythe, who missed the first 54 games of the season after having a bone removed from his left foot in Spring Training, is hitting .290 in 31 at-bats with four extra-base hits and four RBIs in his first nine games since joining the team from Triple-A Tucson.