Upton, whose 10-game hitting streak ended Friday, was hitless in his first three plate appearances on Saturday before getting a single as part of the Padres' four-run ninth inning that tied the game at 6.
The Padres are currently carrying four outfielders, and Venable is the most likely candidate to see playing time in the event Upton needs more time to rest his quad. Cory Spangenberg can play the outfield in a pinch, as can Alexi Amarista.
Upton is hitting .326 this season in his first 46 at-bats with a team-leading three home runs. He ranks second in RBIs (eight) to teammate Matt Kemp, who has nine and hit his first Padres homer in the first inning on Saturday.