Milwaukee filled their places on the roster by recalling right-handers Trevor Kelley and Miguel Sanchez from Triple-A Nashville. The moves come as the Brewers began a season-high 11-game, 10-day road trip at San Diego.
Manager Craig Counsell said Hader will miss the entire three-game series at San Diego to be with his wife, who is expecting their first child.
"Josh's wife has had complications with her pregnancy and they're at a stage where Josh did not feel comfortable leaving,'' Counsell said before the series opener.
Beyond this series, Hader will take his situation day-by-day, Counsell said.
Peralta left the Brewers' 8-2 loss to the Washington Nationals on Sunday in the fourth inning with tightness in the upper area of his shoulder. Counsell said after Sunday's game that Peralta would go on the injured list and undergo an MRI on Monday.
"I was feeling it a little bit earlier, but that inning it got worse," Peralta said after the game. "That's why I made the decision to let them know and why I came out of the game."
Peralta, who turns 26 on June 4, is 3-2 with a 4.42 ERA and 50 strikeouts in 38⅔ innings this season. He made the All-Star team last year and went 10-5 with a 2.81 ERA and 195 strikeouts in 144⅓ innings.
Hader, 28, is off to a spectacular start has allowed five walks, two hits and no runs in 15 appearances. He has struck out 21 batters in 13⅔ innings. Opponents are batting .045 against him.
The three-time All-Star has converted 29 consecutive save opportunities, the longest active streak in the majors. His last blown save came July 7 against the New York Mets.