Holland will make his season debut Wednesday against the Oakland Athletics. Harrison left Thursday's game in the fifth inning and is dealing with biceps tendinitis.
The Rangers will wait to make the roster moves official, preferably not until Holland is scheduled to pitch. Washington said that approach could change depending on how a relatively fresh bullpen fares Saturday against the Kansas City Royals.
Holland now has the opportunity to pitch his way into the rotation. He's been dominant through six starts at Triple-A Oklahoma City at 4-1 with a 0.93 ERA. He has struck out 37 and walked just seven.
"He's been throwing the ball extremely well, commanding his fastball, and his secondary pitch is getting him over," Washington said. "I think the numbers explain what he's been doing."
Harrison said he could pitch through the injury if it was later in the season, but the team is taking a cautious approach.
"I'm not concerned. It's just tendinitis, a bunch of guys have had it," Harrison said. "If it was August, September, I would just throw through it, but right now they just want to get that out of there so I can be healthy for the rest of the year."
Washington would not say whether Holland would remain in the majors once Harrison returns.
"Let's let him get here, get him in there and then see what happens," Washington said. "But, it's obvious he's one of the guys we've been trying to get up here for a while."
Last season, his first in the majors, Holland was 8-13 with a 6.12 ERA. He appeared in 33 games and started 21.