The top job at Ferrari, a high-profile name in Formula One car racing, will be taken over by the head of parent group Fiat, Sergio Marchionne, Fiat said in a statement.
A press conference held by Montezemolo and Marchionne was announced for Wednesday afternoon.
Ferrari has been unsuccessful in Formula One racing for six years.
"Our desire to see Ferrari express its full potential on the track led to certain mutual misunderstandings that were voiced publicly this weekend," Marchionne said in a statement Wednesday.
"I want to personally thank Luca for everything he has done for Fiat, for Ferrari, and for myself," he said.
Ferrari is a subsidiary of the Fiat Group, which Montezemolo, aged 67, chaired from 2004 until 2010.
On Saturday, Montezemolo had publicly stated he wanted to spend another three years in the job.
Marchionne was also quoted at the weekend saying no changes in Ferrari's management were planned but adding, "no one is indispensable".
"Montezemolo's business record is very good but in the case of Ferrari, a leader must also be judged on sporting results," he had said.
At the opening of the Milan stock market, Fiat shares climbed 2.79 percent to €7.91.
Fiat said Montezemolo would leave the job, 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.
"An era is ending, and I have decided to leave the presidency after 23 marvelous and unforgettable years," Montezemolo said in a separate statement.