Reports in the Indian press suggested officials at the Board of Control for Cricket in India had considered bringing forward their series in England, which is due to begin on August 4 and end on September 14 to create a viable window.
"I am advised that the Indian government is of the view that playing the IPL while the population is in lockdown provides a few hours of joy and respite each day," he added.
"That's certainly something that we will talk about when I get a chance to sit down with the team," Ponting said of the off-spinner, who had gone 47-1 against Mumbai in the previous match.
"His report from the second COVID test, came positive," the 2020 IPL finalists said in a statement. "He is currently in isolation at a designated medical care facility."
Participants will have to stay in restricted health environment for this year's IPL, which will be played across six venues, initially without spectators, from Friday.
"(Archer) had a further injection for the right elbow injury that had seen him declared unfit for selection for the current ODI series versus India," the ECB said in a statement.
"The procedure on Jofra's hand will take place on Monday... so he can recover during the planned break following his elbow injection.