He's expected to receive the results on Monday, but the Twins are worried the 23-year-old could need Tommy John surgery.
Gibson, who is expected to fly to Minneapolis on Sunday, will have the results of his MRI examined by team physicians John Steubs and Daniel Buss on Thursday.
Gibson, a 6-foot-6 right-hander who was the club's first-round Draft pick in 2009, had his start with Triple-A Rochester skipped on July 27 after experiencing soreness near his elbow. He is 3-8 with a 4.81 ERA in 18 starts this season, with 91 strikeouts and 27 walks over 95 1/3 innings.
"You're always concerned it might be the ulnar nerve," Twins Minor League director Jim Rantz said. "I think we've got to wait until we get a reading from our doctors. But there's enough concern that we're bringing him to Minnesota."
Gibson has been struggling recently, as he went 0-5 with a 6.47 ERA in eight starts over June and July. It came after he entered June with a 3.60 ERA and 59 strikeouts in 55 innings.
Fellow Rochester right-hander Anthony Slama, who was placed on the Minor League disabled list on July 6, is also scheduled to head to Minneapolis for tests on his elbow.
"He's been out a while and doesn't seem to be getting any better," Rantz said.