The organising Indian cricket board (BCCI) and the league's governing council members convened an emergency meeting at which they decided to suspend the tournament with immediate effect.
The BCCI had forged ahead with the league despite fierce criticism for staging it in a country where coronavirus infections surged past 20 million on Tuesday.
"These are difficult times, especially in India, and while we have tried to bring in some positivity and cheer, however, it is imperative that the tournament is now suspended and everyone goes back to their families and loved ones in these trying times," the league said in a statement.
"The BCCI will do everything in its powers to arrange for the secure and safe passage of all the participants in IPL 2021."
The eight-team IPL, with an estimated brand value of $6.8 billion, is the richest Twenty20 league and attracts many of the best players from around the world to cricket-crazy India.
As many as 57 foreign players, including 14 Australians, are currently stuck in India along with dozens of support staff.
IPL chairman Brijesh Patel told Reuters it was too early to say when the league, originally scheduled to culminate in a May 30 final in Ahmedabad, could resume.
"We are looking for another window," Patel said by telephone. "Right now we can't say when we can reschedule it."
A suspension looked almost inevitable after Monday's game in Ahmedabad had to be postponed after two Kolkata Knight Riders players tested positive for COVID-19.
Two non-playing members of Chennai Super Kings also contracted the virus in Delhi, prompting questions about the robustness of the league's bio-bubble arrangements.
The abrupt suspension left foreign players, including England's World Cup-winning captain Eoin Morgan and Australia's Steve Smith and David Warner, with a major headache.
Australia has banned all arrivals from India until May 15 and England has added India to its travel "red" list.
In a letter to the franchises last month, the league assured them they would discuss the foreign players' travel arrangements with the Indian government.
Cricket Australia declined to comment when asked if it had any plans to try and bring its players home.
Hours before the league was suspended, the Australian Cricketers' Association said it would talk to the Australian government about the players' travel plans.
Australian players Andrew Tye, Adam Zampa and Kane Richardson cut short their IPL stints to return home last week.
Former Australia test batsman Michael Slater, now working as a commentator, strongly criticised the Australian government for its decision to ban citizens in COVID-ravaged India from returning home, saying Prime Minister Scott Morrison has "blood" on his hands.
Morrison dismissed Slater's criticism as "absurd" on a TV talk show on Tuesday.
"What we're doing here is we've got a temporary pause in place because we've seen a rapid escalation in the infection rate in people who have travelled out of India," Morrison said on the Nine Network.
The IPL's suspension also casts doubt on this year's Twenty20 World Cup which is scheduled to take place in India in October-November.
The global showpiece tournament could be shifted to the United Arab Emirates if the COVID-19 crisis in India does not ease, a BCCI official said last week.