Harrison, who left Tuesday's game with a stiff back after 1 2/3 innings, was diagnosed with severe nerve irritation in his lower back. He will need spinal fusion surgery to eliminate the discomfort, which would force him to miss the rest of the season.
General manager Jon Daniels said other major league players have returned from such a surgery but it's a much more involved procedure. Harrison missed virtually all of last season after having surgery to repair a herniated disk in his back. At the time, Daniels said doctors told Harrison this could be one of the downfalls of that surgery.
Harrison also could try to rehab the injury and get it to a point where he could pitch through the discomfort.
Harrison has not yet selected an option. The Rangers have placed both him and Perez on the 15-day disabled list.
"The facts are there aren't a lot of guys who've had it and come back successfully," Daniels said when asked whether Harrison's injury is career-threatening.
"I feel for Matt. It's a blow to the club. He's worked extremely hard to come back and done everything by the book and then some. He showed signs he's getting all the way back, but I feel for Matt and his family.
"The odds may not be great, but I'm hoping he's the exception and can make it back."
Perez has a partial tear of the ulnar collateral ligament in his left elbow. He could try to rehab the injury and return in 10 to 12 weeks, if it responds. Or he will need Tommy John surgery, which would force him to miss the rest of the season.
Daniels said he will meet with Perez on Friday.
Harrison, 28, signed a five-year, $55 million deal in January 2013 after winning 18 games. Since then, he's 1-2 with a 5.79 ERA.
In the two seasons before signing his new deal, Harrison was 32-20 with a 3.34 ERA in 62 starts. He pitched nearly 400 innings.
Perez, 22, signed a four-year, $12.5 million deal in November with team options through 2020.
He started the season 4-0 and pitched consecutive complete-game, three-hit shutouts. Then he lost three consecutive games and bore no resemblance to the pitcher who had dominated in April.
After his last start, he complained of elbow irritation.
Daniels said he isn't looking to make a trade to fortify the rotation. For now, he'll go with players already on the roster such as Nick Tepesch, who started Wednesday's 5-4 loss to the Astros, and rookie Nick Martinez, who will be added to the rotation.
The Rangers currently are in fourth place in the American League West, five games behind the Oakland Athletics. In the past 16 games, they have one start of more than six innings from a pitcher other than Yu Darvish.
"You don't change your expectations until you see how team handles it," Daniels said. "Teams deal with injuries all the time.
"I'm not going to sit here now and sell our club short. We still have a lot of good players. It's just more challenging."