The viability of the Games in Japan is in doubt as the country battles to contain the deadly virus.
Teams from more than 20 countries were supposed to take part in the five-day qualifying tournament on March 18 in Bangalore.
"FIBA is now working in close collaboration with the International Olympic Committee on the best solution possible in the circumstances," said the international federation.
The postponement causes problems as the tournament has to take place before the next round of qualifying in Budapest starting April 24.
Nepal's Everest Premier League, scheduled to begin on March 14, has also been called off because of the coronavirus, which has killed more than 3,000 people around the world.
The fourth edition of the Twenty20 league had signed West Indies batting star Chris Gayle, with Afghanistan's Mohammad Shahzad and Sri Lankan batsman Upul Tharanga also due to take part.