The decision came after Flames General Manager Jay Feaster and Sutter had a meeting to discuss a number of issues regarding the team and its future.
"Brent and I explored many options and ultimately determined that it is best to proceed in different directions," Feaster said in a statement.
"On behalf of the Calgary Flames, we sincerely appreciate his hard work, dedication and commitment to our organization, and we wish him every success."
He posted a combined record of 118-90-38 with Calgary, who finished the 2011-12 NHL campaign five points out of the eighth and final playoff spot in the Western Conference.
"After discussions with Jay since the season ended, it was in the best interest of the organization and myself to part ways," said Sutter. "I wish the Calgary Flames all the best."
(Reporting by Steve Keating in Toronto; Editing by Frank Pingue)