The incident in the city of Nashik, one of India's worst-hit areas, happened after the tank of oxygen leaked, said Rajesh Tope, the health minister of Maharashtra, the richest state, where the city is located.
"Patients who were on ventilators at the hospital in Nashik have died," Tope said in televised remarks.
"The leakage was spotted at the tank supplying oxygen to these patients. The interrupted supply could be linked to the deaths of the patients in the hospital."
The world's second most populous nation reported 295,041 new infections on Wednesday - the biggest daily rise reported in any country - stretching its hospitals to breaking point, officials said.
Only the United States had a slightly higher one-day rise of 297,430 cases in January, though its tally has since fallen sharply. India's 2,023 deaths were also its highest in the pandemic.
Adding to the sense of alarm, the Serum Institute of India, which manufactures the AstraZeneca COVID-19 vaccine, said it will be able to raise its monthly output to 100 million doses by July from 60-70 million now, later than its previous timeline of end-May.
The delay could slow India's immunisation drive, which the government has opened for all adults from next month to try to stem the deadly second wave.
Hospitals in Delhi, the capital, and elsewhere have been warning that their supplies of medical oxygen that are given to severely ill COVID-19 patients are running low as cases pour in.
Max Healthcare, the largest private sector healthcare provider in Delhi and its suburbs, said some of its hospitals had barely two hours' worth of oxygen left.
"For the last few days the hospital has been facing serious difficulties in procuring adequate and regular supplies of oxygen," it said in a statement.
"Presently, most of the hospitals in the network are working on dangerously low levels of oxygen supply, which can lead to a very serious adverse patient incident," Max said.
Television showed images of people with empty oxygen cylinders crowding refilling facilities in the most populous state of Uttar Pradesh, as they scrambled to save stricken relatives in hospital.
The situation was so severe that some people had tried to loot an oxygen tanker, forcing authorities to beef up security, said the health minister of the northern state of Haryana.
"From now, I've ordered police protection for all tankers," Anil Vij told Reuters partner ANI.
LOWERING THE GUARD
Health experts said India had let its guard down when the virus seemed to be under control during the winter, allowing big gatherings such as weddings and festivals.
India now faces a coronavirus "storm" overwhelming its health system, Prime Minister Narendra Modi said in a national address overnight, adding that authorities were working with states and private firms to deliver oxygen with "speed and sensitivity".
Modi is himself facing criticism for addressing packed political rallies for local elections and allowing a religious festival to go ahead in which millions take a ritual bathe in the river Ganges, considered sacred by Hindus.
India has so far administered nearly 130 million doses of vaccine, the most in the world after the United States and China but still small relative to its population of 1.35 billion people
Vaccine doses have already run short in many states though inoculations are currently restricted to frontline workers and those aged above 45.