Hendriks, 24, has made three starts with the Twins this year, posting a 3.94 ERA with eight strikeouts and two walks in 16 innings. His last start came in the first game of a doubleheader against the White Sox on Aug. 9, when he gave up two runs in 6 1/3 innings.
Hendriks has a 4.67 ERA in 16 starts at Rochester, but threw eight scoreless innings in last start on Monday. He's fared better of late, with a 3.65 ERA spanning his last 10 outings.
Gibson, meanwhile, is expected to make about two or three starts with Rochester before being shut down, according to Twins assistant general manager Rob Antony. Gibson, who is coming off Tommy John surgery, has thrown 142 2/3 innings combined between Rochester and the Twins this season. He's scheduled to start again on Sunday.
Rhett Bollinger is a reporter for MLB.com. Read his blog, Bollinger Beat, and follow him on Twitter @RhettBollinger. This story was not subject to the approval of Major League Baseball or its clubs.