The Canaries secured their top-flight status earlier this month and have started trimming their squad ahead of next season, with defenders Marc Tierney and Elliott Ward also leaving in the summer.
Norwich have already confirmed that striker Chris Martin will join Derby after making 117 appearances for the club, while youngsters Tom Adeyemi and George Francomb will not be given new deals.
Goalkeeper Lee Camp only joined in January, but will be allowed to leave, and development squad players Ramil Sheriff and Scott Olumide Durojaiye have also been released.
Canadian international Jackson scored 21 goals in 86 appearances and helped fire the club to promotion from the Championship in 2011.
Korey Smith graduated from the club's academy, racking up 73 appearances and four goals, while defender Ward has made 55 appearances and scored one goal, but he did spend last season on loan at Nottingham Forest.
Tierney, who is expected to sign for Bolton, joined from Colchester United in January 2011 and clocked up 39 appearances in his two years at Carrow Road.
Norwich manager Chris Hughton said: "I would like to personally thank every single one of these lads, their attitude this season has been first class. They are all top individuals and we wish them all the very best."