Pietrangelo had already missed Vegas' past four games because of "personal reasons." He has been moved to the Golden Knights' non-roster list.
"The Vegas Golden Knights wholeheartedly support Alex and the Pietrangelos and ask that the family's privacy be respected at this time," the team's statement read.
There is no timeline for Pietrangelo's return.
Vegas coach Bruce Cassidy put his support behind Pietrangelo in a news conference Wednesday ahead of his team's game against the New York Rangers.
"We're supporting him," Cassidy said. "When he's ready, he'll come back."
Pietrangelo's family previously dealt with a health crisis when his niece was diagnosed with a Wilms' tumor -- a rare kidney cancer that primarily affects children -- in 2018. She recovered, and Pietrangelo has been active in charity work raising awareness for children's cancers.
Pietrangelo, the Golden Knights' top-pairing defender, has appeared in 23 games with three goals and 21 points, tied for second most on the team and putting Pietrangelo in the top 10 of point-getters among all NHL defensemen.
The Golden Knights, currently atop the Pacific Division standings, are also without Jack Eichel, day-to-day with a lower-body injury, and forward Brett Howden (also lower-body injury), who was placed on long-term injured reserve on Wednesday.