"When I moved my hand [after being struck], I felt a little break," Perez told MLB.com. "When the doctor said, 'OK, you have to take four weeks,' I said, 'OK, I'm done for this month,' and I set my mind to what I need to do now."
X-rays revealed a fracture of the ulna bone in his left forearm.
"I don't want to think a lot about [the injury]," Perez said. "I just want to be focused on what I need to do to be ready in a couple months and help the team."
Texas general manager Jon Daniels hopes Perez will be able to return to action about a month into the season.
"I feel for Martin -- he looked like he's figuring some thing out," Daniels said. "He'll bounce back. ... We'll look around at external options, but I expect to go internally at this point. Knock on wood -- hope to get [him] back a month into the season, give or take."
The 21-year-old Venezuelan went 7-6 with a 4.25 ERA in 127 innings with Triple-A Round Rock last season. He struck out 69 and walked 56.
He made his Major League debut on June 27, allowing four runs in 2/3 innings against Detroit. In 12 appearances at the big league level with Texas, he went 1-4 with a 5.45 ERA in 38 frames overall.
Perez had been a possible candidate to win the fifth starter job with the Rangers, though now it's not expected he'll throw for about four weeks before rehabbing another month.