Financial Technologies (India) Ltd, founded by Shah and also the flagship firm of his group, is the promoter as well as largest shareholder in the exchange.
In the wake of the NSEL crisis, the group has come under the scanner of multiple agencies including Sebi and FMC.
Shah has put in his papers as non-executive director from IEX board last month. His resignation has been accepted by the exchange's board, a source close to the development said.
The exchange now has 10 members on its board, which is chaired by Venkat R Chary while S N Goel is the CEO and Managing Director, according to its website.
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The exchange, which started operations in 2008, is the country's premier bourse for electricity.
As per its website, the bourse has more than 2,600 participants across utilities from 27 states, f union territories, among others.
Last month, FTIL had announced sale of five per cent stake in IEX for Rs 72.89 crore as part of efforts to comply with the regulatory norms.
Post that transaction, its shareholding in the company would reduce to 28.49 per cent.
Last month, capital market watchdog Sebi had ruled that FTIL was not "fit and proper" to own stakes in any stock exchange and directed it to divest existing holdings in MCX-SX and four other entities.