According to Black, there's a chance Smith -- who sustained the injury in Thursday's victory -- could be ready to get back in the starting lineup during a series in San Francisco that begins on Monday.
Smith suffered the strain chasing a Jose Lobaton double down the left-field line in the 10th inning. The Padres went on to win the game, 4-3, in 12 innings.
"When I was running toward the left-field line, I felt it tweak on me," Smith said. "I've had something similar before in Colorado, where I think I missed three games."
The Padres played their second game two men short on the bench on Saturday, as the reserves were Alexi Amarista, Nick Hundley, and Yasmani Grandal.
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.