Fellow director Andrew Saunders takes over as interim chairman ahead of next month's Annual General Meeting.
Perry said: "I would like to thank the fans - the heartbeat of the club. I cannot praise them highly enough."
Perry, Saunders and Steve Middleton, who are all long-standing Stags supporters, bought the club from Keith Haslam in the summer of 2008, shortly after Mansfield were relegated from the Football League.
My decision to leave will not stop the growth of the club
Andy Perry
The deal brought to an end 15 years in charge for Haslam, and at the time, Saunders described taking over as a "boyhood ambition".
Perry, whose resignation takes immediate effect, said: "My decision to leave will not stop the growth of the club.
"The club still requires the backing of the whole town."
Source: BBC Sport
Source: BBC Sport