The Sky Blues, relegated from the Championship this summer, have drawn their first three games since beginning life in the third tier for the first time since 1964.
Thorn, 45, replaced Aidy Boothroyd in April 2011 following a stint as caretaker. The club will now begin their search for their 12th manager since relegation from the Premier League in 2000.
Richard Shaw and Lee Carsley are joint caretaker managers.
Chief executive Tim Fisher told the club's official website: "We have not taken this decision lightly. We recognised that last season there were off-the-field matters that affected team affairs and felt it was right and proper to give Andy the chance to put that right over the course of the summer and the start of the season.
"We do not feel that has happened. Of course, the fact that we have surrendered the lead in the first three league games has not helped, but there are several other factors in this decision - not just three disappointing results."
Thorn, a member of Wimbledon's FA Cup-winning side in 1988, had seen his side surrender leads in all three of their league games this season against Yeovil, Sheffield United and Bury.