The decision was made at an emergency meeting with the IPL Governing Council and Board of Control for Cricket in India.
An IPL spokesperson says the BCCI does not want to compromise on the safety of players, support staff and others involved in the competition.
Kane Williamson's Sunrisers Hyderabad team mate Wriddihiman Saha has tested positive for Covid-19, making the franchise the third to register positive cases at the IPL.
England cricketers have begun flying home: players including Jos Buttler, Jason Roy and brothers Sam and Tom Curran have either already left or will do so today.
Meanwhile, the New Zealand governing body's liaising with the Indian and England boards and the government to formulate an exit plan for their 10 players.
Kiwi cricket commentator currently in India Danny Morrison joined D'Arcy Waldegrave to discuss what's happening with the players.
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