"Last night, in the heat of the battle, he was fine and after the game he thought he'd be fine," Black said. "But he woke up today and was a little sore."
Alexi Amarista got the start a shortstop for the Padres in the second game of a three-game series.
Black said the Padres will continue to evaluate Cabrera on Wednesday and through Thursday's off-day before a determination will be made before Friday's game against the Giants at Petco Park.
"We'll see how it sets up over the next couple of days," Black said.
Cabrera suffered the injury in the eighth inning after he walked and went to second base on Amarista's fly ball, returning to first base on a play the Reds appealed, saying Cabrera didn't retouch the base.
Cabrera remained in the game and actually started a game-ending double play in the ninth inning that sealed the Padres' 1-0 victory over the Reds, a game where they had just one hit.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.