Right-hander Anthony Swarzak, who was stretched out to six innings during Spring Training, will start in place of Hendriks.
Hendriks took part in Friday's Opening Day ceremonies, but felt sick later that night, and was admitted to the hospital early Saturday and will be kept there until Sunday morning.
"It is amazing," Twins general manager Terry Ryan said with a hint of disbelief. "Everything was fine until he got back home. I don't know what he had, but he's still in the hospital. He'll get out tomorrow morning. It's too bad, because the kid did a wonderful job for us this spring. But it shouldn't take too long to get him back out there."
Hendriks, 23, posted a 2.84 ERA during Spring Training, and was slated to start with right-handers Scott Baker (elbow) and Jason Marquis (family matter) unavailable to open the season.
But instead, the Twins will turn to Swarzak, who also fared well in spring with a 2.93 ERA, and was stretched out to be a long reliever or a spot starter.
"I was preparing to be a starter for weeks in Spring Training, and was put in a situation where if they need a spot start, I'd be ready to go," Swarzak said. "It's unfortunate for Liam to be in the situation he's in. I hope he gets better as soon as possible, because he's a pretty good pitcher, and in the big picture we need as many good pitchers on the staff as we can get."