Robertson, 24, posted a 3.77 ERA with 33 strikeouts in 28 2/3 innings in 33 relief appearances for the Red Wings to earn his first callup to the big leagues.
He said he was told of the decision after Rochester's game on Sunday, as Red Wings manager Gene Glynn held a team meeting to give him the good news.
"It was pretty exciting," Robertson said. "I kinda figured there would be a move made and some guys we're trying to figure out who it was going to be. A couple guys said they thought it was going to be me, but I didn't want anybody to jinx it."
Robertson is now the second lefty in Minnesota's bullpen, joining Glen Perkins. But with Perkins serving as a co-closer, along with right-hander Jared Burton in Capps' absence, Robertson could be used in a situational role against lefties.
"You always say you'd like to break him in a bit and get an easy situation, but that gets thrown out the window when you need him to face a lefty like Adam Dunn," Twins manager Ron Gardenhire said. "He's gotten lefties out down in the Minor Leagues and that's why we brought him up here. He's a bulldog."