Barbashev was a restricted free agent and helped the Blues capture the Stanley Cup in 2019.
Last season, the 25-year-old forward posted five goals and seven assists (12 points) in 38 regular-season games.
In 270 career games over five seasons - all with the Blues - Barbashev has posted 42 goals and 47 assists (89 points).
Remaining restricted free agents still to sign are Dakota Joshua, Jordan Kyrou, Zach Sanford and Robert Thomas.