The outfielder has an ankle injury and Leyland said that's why he had to pinch run for him with Don Kelly in Game 1.
That means yet another key right-handed bat and outfielder is out for the Tigers. Delmon Young was not on the club's ALCS roster because of an oblique injury.
"We're a real resilient team," Leyland said. "Do I like this? Obviously, no. Do I like losing Delmon? Obviously, no. But we're a tough team. We'll figure something out and we'll get through this.
"We're like every other team in baseball that has these type of situations pop up. You get through it. We're not going to sit around and feel sorry for ourselves. I can guarantee you that. We'll make due somehow."
Rangers skipper Ron Washington expects the Tigers to be ready, no matter what the injury situation is with the club.
"They've been resilient all year," Washington said. "Right now, you can't panic. So they'll do what they have to do to fill that roster spot. Knowing Jim Leyland, his team will be ready to play tomorrow. There's nothing you can do about that, but that's why you have guys available that if something happens, you can bring them on."
Ordonez was 0-for-2 with a walk and a strikeout before exiting Game 1. He was 5-for-11 with no RBIs in the ALDS.