Mr Dabengwa tendered his resignation with immediate effect, saying it was “in the interest of the company and its shareholders”.
The fine, which amounts to double MTN’s profit in 2014, was for failing to cut off unregistered mobile users.
The firm was given until November 16 (two weeks), to pay the penalty.
The company is in talks to reduce the fine.
Meanwhile, Non-Executive Chairman, Phuthuma Nhleko, has been appointed Executive Chairman for a maximum of six months, while the company looks for a successor.
Nigeria is MTN’s biggest market, with 28.5 million subscribers, followed by Iran and South Africa.