Assistant Graham Gartland has also left the club, who are bottom of the table with just three points from eight matches going into Saturday’s game against Livingston at the Tony Macaroni Arena.
McCann had been in charge since April 2017 and guided the Dark Blues to ninth place last season but his reign ended on Tuesday evening.
A club statement said: "We have explored alternative options to support the management staff recently but unfortunately these did not come to fruition. We would like thank Neil and Graham for their efforts while in charge and wish them all the best for the future."
