All three are currently playing in the Stanley Cup playoffs, including Nashville's Rinne, who is a finalist for the third time but has yet to win the award.
Rinne, 35, had 42 wins, a 2.31 goals-against average and .927 save percentage in leading the Predators to the Presidents' Trophy for best regular-season record (53 wins, 117 points).
Rinne tied Vasilevskiy for most shutouts with eight, which is also a Nashville team record.
Vasilevskiy and Helleybuyck, both first-time finalists, tied for the league lead with 44 victories.
Vasilevskiy, 23, helped carry the Lightning to their best record (54-23-5) in franchise history with a 2.62 GAA and .920 save percentage.
Hellebuyck, 24, is the first finalist in franchise history and had a 2.36 GAA and .924 save percentage.
The winner will be announced at the 2018 NHL Awards in Las Vegas on June 20.