According to The Australian, Chakravarty left the biosecurity bubble earlier this week to have scans done.
The IPL released a statement confirming Monday's fixture in Ahmedabad had been rescheduled.
"Both the players have isolated themselves from the rest of the squad. The Medical Team is in continuous touch with the duo and are monitoring their health. Meanwhile, the Kolkata Knight Riders have now moved towards a daily testing routine to identify any other possible cases and treat them at the earliest," the statement read.
"The Medical Team is also determining the close and casual contacts of the two positive cases during the 48 hours prior to collection of the sample that returned the positive test results.
"The BCCI and the Kolkata Knight Riders prioritise the health and safety of everyone involved and all measures are being taken in that endeavour."
The Knight Riders are currently seventh on the IPL ladder, having won two of their opening seven fixtures.
The glamorous T20 tournament has proceeded without crowds as the number of coronavirus cases in India escalated at an alarming rate.
Australian cricketers Andrew Tye, Adam Zampa and Kane Richardson returned home last week as India's coronavirus situation worsened.
There were nearly 400,000 new cases registered across India on Sunday in the world's fastest-growing outbreak — the country of 1.3 billion also reported 3689 coronavirus deaths.
A huge international effort is underway to deliver much-needed oxygen to cities around India where coronavirus cases have skyrocketed to the point where people infected, including babies, have died while waiting for treatment outside hospitals.
Long queues were seen at vaccination centres across the weekend, with people desperate to be inoculated against a disease that has overwhelmed the healthcare system.
Social media platforms have been flooded with pleas from people looking for oxygen cylinders, medicines and hospital beds as the Covid-19 wave causes widespread shortages.
Last week, Cummins donated A$50,000 to help the nation fight the outbreak, calling for other players to contribute to the PM Cares Fund.
Speaking to SEN earlier on Monday, Cricket Australia chief executive Nick Hockley said there were no plans to bring the Australian players home via a chartered flight.
"We're working closely and talking closely with the ACA [Australian Cricketers' Association], with the players and with the BCCI [Board of Control for Cricket in India] to make sure everyone's okay and the people have got full information.
"We've been in touch with the players there and they are generally in good spirits.
"The work the BCCI has done around the [biosecurity] bubble means they are feeling safe and secure, and those we've talked to are generally planning to complete their playing commitments.
"The BCCI have come out and said they understand and want to support the players in making sure they get home safely at the end.
"The tournament doesn't finish until the 30th of May, so for the moment it's monitor the situation and as we get closer to the end of the tournament we'll need to see where the situation is at."
Last month, Australian all-rounder Daniel Sams tested positive to Covid-19 while in hotel quarantine after arriving in India.
