Ritchie signed a one-year contract with Karpat of Finland's Liiga on Saturday, per Chris Johnston of The Athletic.
Ritchie was released from his professional tryout by the Blues on Friday, Lou Korac of NHL.com reports.
Ritchie inked a professional tryout agreement with St. Louis on Thursday.
The Flames acquired Ritchie and Troy Stecher from the Coyotes in exchange for Brett Ritchie and Connor Mackey on Friday.
Ritchie scored a goal on three shots, blocked four shots and added two PIM in Saturday's 2-1 overtime loss to the Ducks.
Ritchie logged a pair of assists and five hits in Thursday's 5-0 win over the Blues.
Ritchie found the back of the net in a 6-2 loss to Philadelphia on Thursday.
Ritchie has racked up four helpers through his last five games.
Ritchie exited Saturday's loss to Tampa Bay with an apparent wrist injury, Wes Gilbertson of the Calgary Sun reports.
Ritchie logged an assist and four hits in Monday's 4-3 shootout loss to the Predators.