The fight was scheduled to take place at Tottenham Hotspur Stadium on Saturday, 20 June.
A statement from Joshua’s promoter Matchroom Boxing said a new date for the fight "was being worked on".
Matchroom added it was "continuing to explore the possibility" of hosting the bout at the same venue at a later date.
Joshua, 30, has not fought since December, when he gained a unanimous points victory over Andy Ruiz Jr in Saudi Arabia to regain his belts after losing to the American-Mexican in New York last June.
Pulev, 38, is the mandatory challenger to Joshua's IBF belt. He was scheduled to fight Joshua in October 2017 at Cardiff's Principality Stadium but had to withdraw less than two weeks before the bout because of a shoulder injury.
All fights overseen by the British Boxing Board of Control until the end of May have been suspended because of the coronavirus pandemic.
Promoter Eddie Hearn had previously said Joshua v Pulev could be moved to July because of the uncertainty of when Tottenham's remaining home Premier League matches would be played.
The statement from Matchroom Boxing comes shortly after the Premier League announced that the football season would be suspended indefinitely.
Britain's Tyson Fury, the holder of the WBC heavyweight belt - the only one Joshua does not hold - is contractually obliged to have a third match with American Deontay Wilder.
Fury beat Wilder with a seventh-round technical knockout in Las Vegas in February and promoter Frank Warren has said they could fight again in October.
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