Nelson is 10-2 with a 1.46 ERA in the minors with 114 strikeouts and 32 walks in 111 innings. He started once in the majors this year, getting his first big-league win last month, beating Miami 7-1.
The right-hander takes the rotation spot of Marco Estrada, who was bumped to the bullpen after allowing a league-leading 27 homers in 18 starts.
To make room for Nelson, the Brewers placed left-handed reliever Wei-Chung Wang on the 15-day disabled list after Thursday's 9-1 loss to Philadelphia with shoulder tightness. Wang was a Rule 5 selection from the Pittsburgh organization.
Milwaukee has lost nine of its last 10 games.