The Italian Formula One outfit have struggled for pace so far this season, with Mercedes leading the way in the opening three races in Australia, Malaysia and Bahrain.
Despite boasting two former world champions in the shape of Kimi Raikkonen and Fernando Alonso, Ferrari currently sit fifth in the constructors' championship, and Domenicali felt a change was necessary.
In a statement released on Friday, he said: "There are special moments that come along in everyone's professional life, when one needs courage to take difficult and very agonising decisions. It is time for a significant change.
"As the boss, I take responsibility, as I have always done, for our current situation. This decision has been taken with the aim of doing something to shake things up and for the good of this group of people that I feel very close to.
"With all my heart, I thank all the men and women in the team, the drivers and the partners for the wonderful relationship we have enjoyed over all these years.
"I hope that very soon, Ferrari will be back where it deserves to be.
"My final words of thanks go to our president (Luca Di Montezemolo), for having always supported me and to all our fans. I only regret that we have been unable to harvest what we worked so hard to sow in recent years."
Having joined the manufacturer 23 years ago, Domenicali rose through the ranks and replaced Jean Todt as team principal in 2008.
The team secured the constructors' championship during his first season in charge, but have since failed to find success.
Ferrari president Di Montezemolo paid tribute to the outgoing Domenicali, who will be succeeded by the company's North America CEO Marco Mattiacci.
"I thank Stefano Domenicali, not only for his constant dedication and effort, but also for the great sense of responsibility he has shown, even today, in always putting the interests of Ferrari above all else," said Di Montezemolo.
"I hold Domenicali in esteem and I have watched him grow professionally over the 23 years we have worked together, I now wish him every success for the future."