Gibson played long toss from 120 feet and threw in the bullpen Friday. He'll try to start Tuesday in Kansas City.
The right-hander originally was scheduled to pitch Wednesday against Cleveland but was scratched the day before due to lower back stiffness. Gibson is 8-8 with a 4.19 ERA in 19 starts.
Darnell, who was 5-5 with a 3.43 ERA for Rochester, will be making his first major league start. To make room for Darnell, Minnesota optioned shortstop Jorge Polanco to Double-A New Britain.
Gibson isn't the only Twins pitcher dealing with an injury.
Phil Hughes left Thursday's start after taking a line drive off his shin. He felt better Friday and expects to make his next start.
Kohl Stewart, the No. 4 overall pick in last year's draft, went on the seven-day disabled list Friday at Class A Cedar Rapids with a sore shoulder, but general manager Terry Ryan said he didn't think it was too serious.
The Associated Press contributed to this report.