Chris Jordan and Rashid Khan have had their IPL plans postponed "until further notice" by the Board of Control for Cricket in India (BCCI).
The tournament, which was scheduled to begin on 29 March at the Wankhede Stadium, was initially deferred to 15 April due to the ongoing Coronavirus pandemic.
However, just two days after Indian Prime Minister, Narendra Modi announced the country's lockdown would be extended until at least 3 May, it is now unclear if or when the 2020 IPL will take place.
In a statement, the BCCI said: "The health and safety of the nation and everyone involved in our great sport remains our top priority."
The BCCI added that all parties involved had agreed that the tournament "will only commence when it is safe and appropriate to do so".
Jordan was purchased by Kings Punjab XI and Khan was returning to Sunrisers Hyderabad, while Jofra Archer, who was set to spend a third spell with Rajasthan Royals, had to pull out of the tournament through injury in March.