Wood was placed on the 7-day injured list at Triple-A St. Paul on Saturday due to a right forearm strain, Brandon Warne of Access Twins reports.
Wood signed a minor-league contract with the Twins on Thursday, Aaron Gleeman of The Athletic reports.
Wood (elbow) elected free agency after clearing outright waivers Saturday.
Wood underwent surgery on his right elbow Monday, Chris Halicke of SI.com reports.
Wood (elbow) was transferred to the 60-day injured list Friday.
The Rangers placed Wood (elbow) on the 10-day injured list Tuesday.
Wood (elbow) will undergo an MRI after leaving Saturday's game, Manny Randhawa of MLB.com reports.
Wood was removed from Saturday's game against the Astros with right elbow tightness.
Wood allowed two runs on two hits and struck out one over 1.1 innings in Saturday's 6-5 loss to the Astros.
The Rangers selected Wood's contract Saturday from Triple-A Round Rock.