Hader missed the Brewers' past five games to be with his wife, Maria, for the birth of the couple's first child, Lucas.
The left-handed Hader, who is having another dominating season, picked up his 20th save in Monday's 2-0 Brewers victory, as Milwaukee (39-30) moved ahead of St. Louis (38-31) for sole possession of first place in the NL Central.
Hader has an 0.87 ERA in 22 appearances this season, recording 34 strikeouts in 20⅔ innings.
The Brewers are down another member of their starting rotation, however, as left-hander Aaron Ashby was placed on the 15-day injured list with left forearm inflammation. Ashby left his last start on Thursday against the New York Mets in the fifth inning because he was experiencing tightness in his left forearm. Ashby joins fellow starting pitchers Freddy Peralta and Brandon Woodruff on the IL.
Ashby is 1-5 with a 4.25 ERA in 14 appearances (eight starts) this season.