Elango, who was named interim chief executive in August 2012 when the firm's face Rahul Dhir resigned, cited "personal reasons" for the decision to step down, Cairn said in a statement.
The move came as a surprise as Elango, under whom Cairn touched 200,000 barrels per day of output from its showpiece Rajasthan oilfields, was widely tipped to become the full-time CEO of the company.
Last year, Elango was given a 40 per cent hike in salary, suggesting that he would be taking on a larger role within the company but promoter Anil Agarwal group continued him as interim CEO.
Cairn said the company board has accepted Elango's resignation and added Sudhir Mathur, chief financial officer, has taken over additional charge as interim CEO.
"Tom Albanese, CEO Vedanta Resources plc, and Mike Yeager, Chairman, Operations Review Board, Cairn India, will continue to work closely with the leadership team in managing the business under the guidance of the Board," the statement said.
With Elango, the entire top management of Cairn India has quit the company since billionaire Anil Agarwal-owned Vedanta in 2010 announced buying majority stake in the firm from Scottish explorer Cairn Energy Plc.
Rick Bott, who was Executive Director and Chief Operating Officer of Cairn India, quit the firm on June 15, 2011, while its Executive Director and Chief Financial Officer Indrajit Banerjee resigned with effect from August 23, 2011.
David Ginger, Cairn India's director of exploration and new ventures, quit the firm shortly after that and Dhir put in his paper after the Cairn-Vedanta deal was completed. Company's Director, Commercial and New Business Ajay Gupta quit the firm in January 2013.
In February this year, Sundeep Bhandari, the man credited with laying the foundation and then building what is now Cairn India, quit the company. He along with Dhir, Bott, Banerjee and Ginger ran the firm before Vedanta took over.
Vedanta completed the USD 8.67 billion acquisition of Cairn India in December 2011.
Mathur came in from Aircel after Dhir quit.