Manager Paul Lambert said: "After nearly six years solid service we're grateful for his efforts."
Jamie Cureton, Paul McVeigh, Danny Kelly and Damon Lathrope have also been told their futures lie elsewhere.
Lambert added: "Gary has done really well for us and played a big part this season.
What the hell is going on? I would have put him in my top three players at Norwich this season. I bet he goes to another Championship club. Can't believe it, and am gutted.
Forgot_My_Lines
"He came back really strongly after being dropped early in the season and got himself into the team on merit after some excellent performances."
Doherty was appointed club captain by former manager Bryan Gunn at the start of the campaign, but Lambert took over and made Grant Holt skipper almost immediately.
He was subsequently dropped from the starting 11, but after injury to Michael Nelson he regained his place and was almost ever-present for the rest of the season.
The former Luton and Spurs utility man was City fans' player of the season in 2006, and finished third in the voting this season.
Cureton and McVeigh were both in their second spells with City, but neither had made an impression on the first team under Lambert.
Kelly and Lathrope both graduated though the Canaries' youth setup before being handed professional deals but neither made a first-team appearance.
Source: BBC Sport
Source: BBC Sport