The Florida Panthers selected Montembeault in the third round (No. 77) of the 2015 NHL Draft after he won 33 games for Blainville-Boisbriand of the Quebec Major Junior Hockey League.

After playing two more seasons with Blainville-Boisbriand, Montembeault turned pro and played the 2017-18 season with Springfield of the American Hockey League, where he went 13-23-1 with a .3.25 goals-against average and .896 save percentage.

Montembeault would spend most of the following season with Springfield before being recalled by Florida on Feb. 17, 2019. He made his NHL debut on March 2, making 22 saves in a 4-3 overtime loss to the Carolina Hurricanes. Six days later, he got his first NHL win, making 25 saves in a 6-2 win against the Minnesota Wild.

Montembeault ended the 2018-19 season 4-3-2 with a 3.04 GAA and .894 save percentage.

The Panthers kept Montembeault on the roster at the start of the 2019-20 season as the backup to newly signed Sergei Bobrovsky, but he wound up splitting the time between Florida and Springfield to get more playing time. He finished the season 5-5-1 with a 3.34 GAA and .890 save percentage.

Montembeault was claimed off waivers by the Montreal Canadiens from the Panthers on Oct. 2, 2021, and signed a three-year, $9.45 million contract ($3.15 million average annual value) Dec. 1, 2023, a deal that began the following season. He set an NHL record for saves in a season-opening shutout with 48 in a 1-0 win against the Toronto Maple Leafs at Bell Centre on Oct. 9, 2024. It was also the second most by a Canadiens goalie in a shutout behind Jacques Plante's 52 in a 2-0 victory at the Chicago Black Hawks on Nov. 13, 1955.

Montembeault was named to Canada's roster for the 4 Nations Face-Off during the 2024-25 season.