"Derek's a little banged up," manager Bud Black said.
Norris, who was available to pinch-hit if needed Wednesday, would then get Thursday's off-day to rest his ankle even more before the team opens a series at home Friday against the Rockies.
Norris was catching when a foul ball caught him flush on the ankle in the sixth inning of a 14-3 loss to the Astros.
The day off on Thursday comes at a good time for the Padres, who, after Wednesday, will have played 23 games in 24 days. They're among the Major League leaders in games played.
"It's good for everyone," Black said of the off-day. "I think that we've played the most games in all of baseball. It's good, because we've played a lot of games here early. It gives the fellas a full day. Off-days at home when you're not traveling are good."
Outfielders Matt Kemp and Wil Myers and third baseman Will Middlebrooks have played in all 23 games this season. Outfielder Justin Upton and first baseman Yonder Alonso have missed one game, as has Norris.
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.