The Rangers placed Perez on the 10-day disabled list on Saturday.
The injury occurred Thursday night when the team arrived in New York.
"My bullpen is [Saturday] and I'm going to throw it," he said. "And I'm not going to miss a start. As long as I can hold on to my glove and kind of defend myself, I am going to pitch."
Perez said his thumb got caught against the door jam in his room after someone opened the door. A team trainer took Perez to a hospital where the nail was reattached and X-rays showed a small fracture.
Perez's next start is scheduled for Wednesday in Cleveland.