The club made the statement on Monday night.
The Flames say the move allows the club to continue to work with his agents toward a deal, presumably with a longer term.
The move also means Tkachuk can't accept a $9 million qualifying offer.
Tkachuk, 24, is coming off a three-year, $21-million deal with the Flames, who drafted him sixth overall in 2016.
Last season, Tkachuk posted a career-best season, scoring 42 goals to go with 62 assists for 104 points in 82 games. The Flames ultimately fell in Round 2 to the Edmonton Oilers in the playoffs, where Tkachuk produced 10 points in 12 games.
In 431 games across seven seasons, all with Calgary, Tkachuk has 152 goals and 230 points — ranking second in his draft class with 382 points, behind only Auston Matthews.
The move comes after former Flames star Johnny Gaudreau opted to leave town, signing a seven-year deal with the Columbus Blue Jackets as an unrestricted free agent.