The Blues said Wednesday that Bouwmeester was having tests performed and the outlook was positive.
"Jay Bouwmeester is doing very well at the UCI Irvine Medical Center in Anaheim," St. Louis general manager Doug Armstrong said in Las Vegas. "Jay is currently undergoing a battery of tests to determine the how and why of what happened last night but things are looking positive."
Bouwmeester was taken from the bench on a stretcher and the game was stopped with 7:50 remaining in the period at Honda Center in Anaheim. The 36-year-old was conscious and alert when he was taken to the hospital.
"Thankfully, with the quick response of our medical trainers, Anaheim medical trainers and their team physicians, they were able to stabilize Jay," the Blues said in a statement. "He was alert and moving all of his extremities as he was transported to UC Irvine Medical Center."
The game, which was tied 1-1, will be rescheduled. Neither team spoke to the media afterward.
"Tonight's game between the St. Louis Blues and Anaheim Ducks has been postponed by the NHL due to a medical emergency that occurred at 12:10 of the first period involving defenseman Jay Bouwmeester," the NHL said in a statement. "A decision on when the game will be played will be made in the near future."
The Blues are scheduled to play at the Vegas Golden Knights on Thursday.
Bouwmeester came off the ice after completing a shift and collapsed on the bench. He was playing his 1,241st NHL game; he has played eight seasons for St. Louis and won the Stanley Cup for the first time last season.
He has nine points (one goals, eight assists) in 56 games this season, and 424 points (88 goals, 336 assists) for the Blues, Florida Panthers and Calgary Flames since the Panthers selected him with the No. 3 pick in the 2002 NHL Draft.
The NHL has postponed a game for a medical emergency involving Rich Peverley of the Dallas Stars against the Columbus Blue Jackets on March 10, 2014, and involving Jiri Fischer of the Detroit Red Wings against the Nashville Predators on Nov. 21, 2005.