The duo will not be retained by the club along with midfielder Marco Caligiuri and defender Radoslav Zabavnik.
They join centre-half Jan Kirchhoff, who has signed a pre-contract agreement with Bayern Munich, in having their exits from the Coface Arena this summer confirmed.
"These were human painful decisions but we have decided to make changes," general manager Christian Heidel told a press conference.
Midfielder Ivanschitz has made 29 appearances for the Karnevalsverein this season, scoring six goals and providing six assists, with Caligiuri featuring 21 times and Zabavnik making 15 appearances.
Striker Klasnic has had less of an impact since his much-heralded move from Bolton in the summer, playing just three times.