"We needed someone available now," Royals manager Ned Yost said. "And we're going to Detroit and they have a lot of right-handed hitters."
Finnegan, in a corresponding move, was optioned back to Double-A Northwest Arkansas.
"He did not pitch his way off the team," Yost said of Finnegan. "I thought he pitched really well here. He got his fastball up to 97 [mph] with a really great slider."
Hochevar's return marked his first time on the 25-man roster since 2013, when he posted a 1.92 ERA in 58 games out of the bullpen. He pitched a scoreless sixth inning on Thursday, striking out two batters in the Royals' 7-4 win.
Hochevar had Tommy John surgery in March 2014.
"To finally get back after a long grueling year of rehab, it's exciting," said Hochevar, who got the call about his return Wednesday night and immediately hopped in his car and drove to Kansas City.
As for his rehab experience in Omaha, Hochevar said, "I felt good. Early on I had a little dead arm. But I took the appropriate steps to get my strength back, and kind of harness everything.
"I talked to [Royals pitching coach] Dave [Eiland] and he said just pound the ball down in the zone on both sides of the plate. And just focus on that one thing."
Hochevar said he doesn't expect to be protected by Yost and feels he could start throwing on back-to-back days, though he hasn't done that during his rehab.
"I feel good enough to," he said. "The day after I pitch I feel great.
"... I'm good to go. It's time to get the training wheels off."
Jeffrey Flanagan is a reporter for MLB.com. Follow him on Twitter at @FlannyMLB. This story was not subject to the approval of Major League Baseball or its clubs.