Besides Shah, who is the vice-chairman and shareholder director of the exchange, the bourse's Managing Director and CEO Joseph Massey also put in his papers.
Massey also resigned as shareholder director from MCX-SX CCL (Clearing Corporation Ltd), according to an MCX-SX statement.
The high profile exits come at a time when Financial Technologies-promoted National Spot Exchange Ltd (NSEL) is facing crisis due to non-payment of dues to 13,000 investors.
Last week, the Forward Markets Commission (FMC) had issued show cause notices to Shah and Massey, among others questioning whether they are "fit and proper" to be shareholders and directors of the group's commodity futures exchange MCX.
While renewing the licence of the MCX-SX, which started operations in February this year, capital market regulator Sebi recently directed it to strengthen its governance structure.
MCX-SX said Sebi has nominated former LIC chief Thomas Mathew T as the bourse's Public Interest Director.
"As an interim arrangement, U Venkataraman, whole-time Director, will assist a Special Committee of Public Interest Directors in carrying out the functions of the exchange," it said.
Last month, the Securities and Exchange Board of India (Sebi) asked MCX-SX to constitute a panel of two independent directors and three institutional investor nominees to oversee key business decisions, policy matters and appointments of top management.
In the wake of the NSEL fiasco, Financial Technologies is under the scanner of multiple agencies, including CBI, for alleged violations of various laws.