Villarreal experienced weakness in the elbow after throwing 18 pitches on Sunday against the Rangers.
"The MRI showed basically some inflammation in and around the flexor where it attaches," Rand said. "There's no major structural damage there. It's something that we just have to try to get quiet."
Rand said Villarreal would be examined by Dr. John A. Steubs, the Twins' director of medical services, then be treated symptomatically until he's ready to pitch again. The right-hander likely won't make an appearance in Detroit's three-game series with the Twins, manager Jim Leyland said.
"We have this series and then an off-day [Thursday], so we'll probably back him off," Leyland said. "Pitch him on Friday. There's nothing wrong."
Villarreal said he initially felt the weakness shortly after the All-Star break. He has posted a 2.41 ERA with 48 strikeouts in 37 1/3 innings, but has struggled lately. The 25-year-old has surrendered five runs on five hits in 2 1/3 innings, spanning his last three appearances.
"He doesn't have a complaint of pain," Rand said. "It's a complaint of fatigue. So we just have to give him a couple of days and treat him symptomatically until we feel comfortable about him playing catch again."