The 25-year-old goalie was 16-14-3 with a 2.62 goals-against average, .916 save percentage and two shutouts in 35 games (31 starts) last season.
Among rookie goalies who played at least 10 games, Shesterkin was third in games, tied with Kaapo Kahkonen of the Minnesota Wild for third in wins, fourth in save percentage and fifth in GAA. He was fifth in voting for the Calder Trophy, awarded to the NHL rookie of the year.
"It's huge," Rangers defenseman K'Andre Miller said Monday. "'Shesty' is everything for us. He's been unreal. I've only played with him this past year, but the things he's doing, his work ethic off the ice, is just as good as his work ethic on the ice. He's literally our backstop. He's a great leader."