Barker's contract was selected by the Brewers prior to the second game of Monday's doubleheader against the Cubs.
Barker has pitched in Nashville over the last two seasons, and he's posted a 2.69 ERA, 96:18 K:BB and 0.91 WHIP in 80.1 innings over 70 relief appearances with the Triple-A club. The right-hander hasn't yet made his major-league debut but will provide an additional option out of the bullpen during Monday's nightcap.