Lance Batchelor will remain with the fast-food group until the end of April.
The group's shares plunged more than 9% in early trading and there was little recovery as they closed the day down 49p to 480p.
The announcement came as a blow to investors as Mr Batchelor has helped drive impressive sales and results.
Stephen Hemsley, chairman of Domino's Pizza, said: "Lance has been offered a new role in a significant private equity-backed company and as a result has tendered his resignation.
"His new company operates in a non-competing sector."
Mr Batchelor joined Domino's as a non-executive in 2010 and was appointed chief executive at the end of 2011.
The group posted a 10.3% hike in underlying half-year profits and has succeeded in driving a sharp rise in online sales, which now account for 62.4% of UK deliveries.
Sahill Shan, analyst at N+1 Singer, said Mr Batchelor's departure was "not good news" as Domino's also beds in a new finance boss.
It has recently hired Sean Wilkins as chief financial officer designate to replace Lee Ginsberg, who is retiring at the group's AGM next year.
Mr Shan added the change at the top "creates further uncertainty" amid reports that Domino's is slowing the pace of its UK expansion plans.
The Domino's business in Europe, which is separate from its counterpart in the US, has 833 outlets including 746 in the UK but has recently been hit by problems in its German arm.