The 24-year-old Segura learned his son, Janniel, had died after the Brewers' 7-6 loss to the St. Louis Cardinals on Friday night.
Segura's mother, who attended the game, told several Brewers' wives. They passed the news to their husbands, who then told Segura after the final out.
Brewers Manager Ron Roenicke closed the Milwaukee clubhouse to reporters after the game Friday, and he appeared equally saddened a day later. He kept the clubhouse closed before Saturday's game.
"I didn't know what to say to him other than giving him a hug and telling him we're there for him," Roenicke said. "He had a tough time."
Zimmermann left Friday night's start against Philadelphia after 3 1/3 innings because of a right biceps injury. The roster change was announced Saturday.
Alvarez, a first-time All-Star, is 6-4 with a 2.63 ERA and three shutouts in 19 starts. He pitched a no-hitter against Detroit on the final day of the 2013 regular season.
Callaspo on DL