Mumbai's 1,400 schools closed for a 10-day period starting Thursday to combat the spread of influenza A (H1N1), or swine flu.
India's health minister, Ghulam Nabi Azad, called for calm, as more people took to wearing surgical masks on the streets and flocked to medical centres for testing.
The central and state governments were taking "all possible measures", he told reporters, adding: "Only those people who have symptoms need to wear a mask."
Subedar Awadhpal, headmaster of Hindi High School, echoed some of the public concerns about children’s safety. "The children aren't very careful," he said. "They don't know how to protect themselves. It's in their nature to touch everything, mess around, hug each other. That's what makes them vulnerable to swine flu."
About 2,000 people have been confirmed to have the virus across the country, the health ministry said.
Two people have died in Mumbai.
The city of Pune, some 120 kilometres south-east of Mumbai, has been the worst hit Indian city, with 12 deaths and a cluster of infections.
Mumbai's authorities have decided to give the Tamiflu antiviral drug to all suspected cases, even before their diagnosis is confirmed.