Norris was hurt in the third inning Friday as he reached on an infield single, beating out second baseman Kolten Wong's throw to first base.
On the play, Norris tumbled over first baseman Xavier Scruggs, as the throw from Wong took him into Norris' path. Norris stayed on the ground for a minute and then was examined by a Padres trainer, who was accompanied by Murphy. He remained in the game.
Murphy said Norris was checked out after the game and again Saturday morning.
"The doctors said [the sprain] can't get any worse," Murphy said. "I think he's going to go through periods of being sore. [The training staff] thought he would be more sore today."
Norris ranks second in the big leagues in innings caught this season (614 1/3), trailing St. Louis catcher Yadier Molina (633 innings).
• Pitcher Brandon Morrow, on the disabled list since May 3 with inflammation in his right shoulder, threw a 40-pitch bullpen session before Saturday's game and said he felt good. He'll advance to throwing a simulated game next week, when the Padres are in Pittsburgh, with a rehabilitation stint in the Minor Leagues to follow, said Murphy.