"I went down there and got some good work in and the leg felt really good, and that's the No. 1 priority," said Norris, who will throw in the bullpen on Tuesday.
Norris will rejoin the rotation later this week, but it's not clear who will be out of the rotation. Rookie Dallas Keuchel threw a complete game in Norris' absence Saturday, but the entire rotation has pitched well over the last week. Astros starters had a 1.88 ERA in their last seven games entering Monday.
Astros manager Brad Mills said a decision will be made Wednesday about the rotation. Norris is still on the 15-day disabled list.
"The plans are pretty well in place and put together, but we're not going any further than that," Mills said. "We'll make an announcement on Wednesday regarding that scenario."