"We're just going to treat him day to day and go from there," Rand said.
The Tigers medical staff is not expecting that to take long.
"We're not thinking it's a long-term situation," Rand said.
Earlier, Valverde said he still felt soreness in the wrist, but that it was a little better than it was last night.
"Last night, when I threw the last pitch, I couldn't move my fingers," Valverde said. "It hurt too bad last night. I couldn't do anything. I'm a guy who wants to compete all the time. Something simple, I'd never shut it down. But last night, I couldn't do anything. ...
"It's better today than yesterday. That's why I think it'll soon go away."
With Valverde out, manager Jim Leyland said he'll use his relievers by matchup when it comes to save situations. Phil Coke earned the save Tuesday night, but Joaquin Benoit filled in for Valverde while he was sidelined with back soreness earlier this season.
Octavio Dotel also has closing experience over his many Major League stops and stepped in to get the save after Valverde's back issues forced him out May 15 at Chicago, though he failed in a save situation a week earlier in Seattle.
Even if he's not closing, though, Dotel has the potential to be a critical piece. If Benoit's closing, or if Benoit's off, Dotel becomes the primary right-handed reliever.
"He's a big key for us right now," Leyland said.