Hellebuyck made 31 saves, allowing two goals in a 3-2 win over Anaheim on Sunday.
Hellebuyck will man the home crease Sunday against the Ducks, Mitchell Clinton of the Jets' official site reports.
Hellebuyck will guard the cage during Thursday's road game against the Stars, Brian Munz of TSN 1290 Winnipeg reports.
Hellebuyck made 26 saves in Tuesday's 5-1 win over Dallas.
Hellebuyck will defend the home net in Tuesday's matchup against the Stars, Mitchell Clinton of JetsTV reports.
Hellebuyck turned aside all 24 shots he faced in Friday's 3-0 win over the Ducks.
Hellebuyck led his team out onto the ice Friday in Anaheim and will start the game, Ducks PA announcer Phil Hulett reports.
Hellebuyck will start Wednesday in San Jose, Scott Billeck of the Winnipeg Sun reports.
Hellebuyck came off the bench and earned a win after stopping all five shots he faced in a 4-3 victory over Columbus.
Hellebuyck will patrol the crease on the road versus Dallas on Thursday, Ken Wiebe of The Athletic reports.