Barton, 34, was suspended for 18 months after admitting a Football Association charge in relation to betting.
He joined the Clarets for a second spell in January after leaving Scottish Premiership side Rangers.
Winger Michael Kightly has also been released but talks are continuing with out-of-contract goalkeeper Paul Robinson and midfielder George Boyd.
Manager Sean Dyche said: "Joey leaves us for the obvious reasons after he has again been a big part of what we have achieved this season.
"Equally, Michael has been a great servant of the club and always a tremendous person to have around the group."
Burnley finished 16th in the Premier League, six points above the relegation zone.
Midfielder Joey Barton has been released by Burnley, one month after being banned from football.