Altuve appeared to have aggravated an injury that forced him out of action for a game last week and caused him to miss three games earlier in the month. He was 0-for-3 and had made a terrific defensive play in the first inning before being removed.
Moore suffered an irritation to the AC joint in his left shoulder after trying to make a diving catch of a pop fly off the bat of Starlin Castro.
Batting with one out in the second and no runners on base, Castro lifted a high popup into shallow right field. Altuve circled under the ball before being called off by a hard-charging Moore, who tumbled as the ball glanced off his wrist. Castro wound up with a double.
Moore remained on his knees for a few moments before rising to his feet and eventually leaving the game with head athletic trainer Nate Lucero. Justin Maxwell moved from center field to take Moore's spot in right, and Brandon Barnes entered the game in center.
Neither Altuve nor Moore is going to play in Wednesday's season finale, but neither injury is considered serious.