Shaw had been away from the team since Thursday to tend to his family situation. The 27-year-old was reinstated prior to the team's opener of a doubleheader versus the St. Louis Cardinals.
"(Ryann) was born with a severe heart condition called hypoplastic left heart syndrome," Shaw said, per the Milwaukee Journal Sentinel. "It's a pretty severe heart deformation. We knew this going in and I knew that she was going to have to have surgery.
"She had open-heart surgery on Friday. There were some complications and they had to go back in Saturday for a couple more surgeries. She's been stable ever since Saturday. She's making steady progress now."
Shaw was traded to Milwaukee from the Boston Red Sox in a package deal for reliever Tyler Thornburg in the off-season. Baseball aside, the trade was beneficial for Shaw as Milwaukee is the home to Children's Hospital of Wisconsin, which specializes in the type of surgery needed by Ryann.