Holland exited against Houston because of tightness in his left shoulder that was later diagnosed as a sprain.
Outfielders Shin-Soo Choo and Ryan Rua also left the 5-1 loss to the Houston Astros early because of injuries.
Holland felt the problem in the back of his shoulder on the last pitch he threw during warmups. The left-hander threw nine pitches, but his velocity was noticeably down.
"The velocity below 90 (mph), and not typical of where Derek is normally at," manager Jeff Banister said. "We felt like that we needed to get in front of it."
Anthony Bass was warming up in the bullpen even before Holland finished the first inning trailing 1-0. Bass allowed one run over five innings.
Holland missed most of last season recovering from left knee surgery. He was slowed by soreness in his left shoulder early this spring, but the Rangers said the latest problem was in a different area.
Choo, who late last season had surgeries on his left elbow and left ankle, was gone after two innings because of spasms in his upper back. Jake Smolinski replaced him in right field.
Rua departed after five innings because of a right ankle sprain his sustained running into the left field corner chasing a ball earlier in the game. Delino DeShields replaced him.
Jed Lowrie homered off Holland, who picked off Jose Altuve at second base just before that.
The Rangers have already been beset by injuries again this year, losing ace Yu Darvish when he needed Tommy John surgery last month.
Texas last season lost 95 games while using the disabled list 26 times (for 22 players). That amounted to 2,281 days lost, 833 more than Arizona, who had the second most, and more than double any other AL team.