Mills observed Saturday as Lee was put through some tests by the medical staff to gauge the extent of the injury. Matt Downs started at first base in place of Lee, who is hitting .297 with four homers and 23 RBIs this season.
"He has point tenderness," Mills said. "We're going to evaluate that moving forward as he gets treatment. We're going to kind of monitor him. It's tender and sore. That's all I'm really prepared to say. We don't think there's a tear or something, but at the same time we want to check things out."
Astros general manager Jeff Luhnow took time away from his Draft preparation Saturday to go to the home clubhouse during batting practice and check up on Lee.
"Clearly, when you lose a productive hitter like that, even just for a few days, it's going to affect us," Luhnow said. "Those are the types of injuries that you may not know right away how long he's going to be out, but if it reaches a point where we think he's going to be out more than a week, then certainly we would consider making a move."