Assistant boss Keith Millen has been placed in charge for the final three matches of the season.
The Dons sit 23rd in the third tier, six points adrift of safety ahead of games with Bradford City, Scunthorpe United and Shrewsbury Town.
Managerial rookie Micciche had been at the helm for just three months, having been brought in to replace Robbie Neilson in January, but he departs after winning just three of his 16 matches.
A statement from the 38-year-old on the Dons' official website read: "This is a club that means a lot to me and my family and I put every ounce of effort into the job. Unfortunately, the fine margins have gone against us and it hasn't worked out in the way we would have wanted.
"I am extremely grateful to the board, staff, players and fans for their tremendous support during my time here. It has been an honour to manage this football club and I would love nothing more than to see it get back to where it belongs."
Micciche's final game in charge was Saturday's 4-0 loss against Southend United - the Dons' fourth defeat in a row.