Perez, 26, suffered the injury last week when he fell at his ranch in Venezuela, according to the Rangers. General manager Jon Daniels said Perez told him he was startled by a bull and fell on the elbow.
The Rangers announced that Perez is expected to be sidelined about four months, meaning he might be able to return around the start of next season.
But the Morning News and other media outlets, citing the Rangers' preference to be cautious with the injury-plagued pitcher, have reported that Perez likely will miss the first month of the season.
Perez went 13-12 last season with a 4.82 ERA in 32 starts. He missed significant time from 2013 to 2015 because of Tommy John surgery in his pitching elbow.