Goalkeeper Conor Brennan, defender Lee Ashcroft, midfielders Julien Faubert, Christopher Johnston, Aaron Splaine, and Alex Henshaw all depart.
The club is willing to consider offers for seven other first-team players.
Offers have been also made to Rory McKenzie and Craig Slater.
Earlier on Monday, however, midfielder Slater posted a message on his Twitter account announcing he had decided to leave Rugby Park - he has yet to find a new club.
A club statement said Killie were willing to consider offers for defenders Conrad Balatoni, Kevin McHattie, Mark O'Hara and David Syme, as well as attackers Tope Obadeyi, Dale Carrick and Kallum Higginbotham.
Skipper Connolly missed the club's Premiership run-in and play-off battle due to a hip operation.
Manager Lee Clark warned significant changes in personnel were required after Kilmarnock retained their top-flight status on Sunday. A 4-0 victory over Falkirk in the Premiership play-off final second leg emphatically assuaged fears of relegation, overturning a 1-0 deficit from the first encounter.
Kilmarnock captain Mark Connolly's contract has been cancelled, while six players have been allowed to move on after their deals expired.