Norris gave Murphy and the Padres a scare when he left Saturday's 8-0 victory over the Cardinals in the eighth inning after he was crossed-up on a pitch from reliever Kevin Quackenbush, as the pitch hit him on the inside of his left wrist.
Norris had X-rays late Saturday, and they came back negative.
"He's sore and swollen, as you would expect it to be 12-to-14 hours later," said Padres assistant general manager Fred Uhlman Jr.
Norris wasn't in the starting lineup for Sunday's finale against the Cardinals, though he wouldn't have been anyway as it was a day game after a night game.
Austin Hedges, who replaced Norris in Saturday's game, got the start on Sunday.
The hope, Murphy said, was that Norris gets a chance to rest the wrist Sunday and then on Monday's off-day, and that he'll be ready for the start of a three-game set Monday against the Nationals in Washington.
Murphy didn't rule out the possibility of Norris playing Sunday.
"You don't want to lose a guy so [important] to your pitching plans," Murphy said. "We're thankful we have a guy like Hedges behind him. Hopefully Derek is available today if needed. If not, with the off-day [Monday], the swelling will go down and he'll be available Tuesday."
Norris entered play Sunday leading all Major League catchers in CCS (catcher caught stealing) with 33, and ranked 12th in getting extra strikes (43) for pitchers, according to Baseball Prospectus.
Offensively, Norris is hitting .338 in his last 20 games, with nine extra-base hits and nine RBIs. He entered Sunday with 42 extra-base hits this season, the most of any catcher in the big leagues.