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The Board of Control for Cricket in India (BCCI) said the move was a "precautionary measure".
The BCCI said it was taking "all necessary steps to ensure that all people related to IPL including fans have a safe cricketing experience".
England players including Ben Stokes and Jos Buttler are due to take part.
On Thursday it was announced that Australia's one-day internationals against New Zealand - which begin on Friday - will be played behind closed doors.
England's Sam Curran, Jason Roy, Chris Jordan, Harry Gurney, Eoin Morgan, Tom Banton, Tom Curran, Moeen Ali and Jonny Bairstow are all also signed up to play in the IPL.
The competition was due to run from 29 March to 24 May.
England start a Test series against West Indies on 4 June and had asked players to be back in the country by 26 May, so it is unclear whether that deadline will have to be moved.
The Indian government has travel restrictions in place as a result of the virus, which was designated a pandemic by the World Health Organization this week.
A host of sporting events including the major tennis tours and golf's PGA Tour have been suspended, while the season-opening Australian Grand Prix has been postponed.
More than 125,000 people have been diagnosed with the virus in 118 countries around the world, according to the WHO. The total number of deaths is more than 4,600.