The top job at Ferrari, a high-profile name in Formula One car racing, will be taken over by the head of Fiat, Sergio Marchionne, the statement said.
Ferrari has been unsuccessful in Formula One racing for six years.
On Saturday, Montezemolo said he wanted to spend another three years in the job.
Ferrari is a subsidiary of the Fiat Group, which Montezemolo, aged 67, chaired from 2004 until 2010.
The statement said he would leave the job at Ferrari, which he has held for 23 years, at his own request at the end of celebrations marking the 60th anniversary of the company's presence in the United States.