All three are looking to win the award for the first time. It also marks the first time all three are making their debuts as finalists since 2014.
Markstrom, in his second season with Calgary, helped the Flames finish first in the Pacific Division. He went 37-15-9 with career bests in goals-against average (2.22) and save percentage (.922).
The Flames are tied 2-2 with the Dallas Stars in a Western Conference quarterfinal.
Markstrom, who had a league-leading nine shutouts this season, is the first Flame to be a finalist for the award since Miikka Kiprusoff in 2006-07. The latter is the only Flame to have won the award -- one year earlier.
Shesterkin was 36-13-4 with a league-leading 2.07 GAA and .935 save percentage. A 2014 Rangers draft pick (fourth round, 118th overall), the Russian broke into the NHL in the 2019-20 season.
This year's Stanley Cup Playoffs, however, have been a challenge for Shesterkin, who has been pulled in two games in a row as the Rangers have fallen behind 3-1 against the Pittsburgh Penguins.
Saros went 38-25-3 with a 2.64 GAA and .918 save percentage, but suffered a foot injury in the final week of the regular season and was inactive for the post-season.
It was a big blow for the Predators, who became the first team to be eliminated from the playoffs on Monday when they were swept by the Colorado Avalanche.
Saros became Nashville's full-time starter this season after the retirement of Pekka Rinne.
NHL general managers voted on the Vezina at the conclusion of the regular season.
The winners of all awards will be announced during the Conference Finals and Stanley Cup Finals.