Local media said almost 100 flights were cancelled, but many more took off.
Maharashtra state, which has India's highest number of Covid-19 cases, said it would only allow only 50 flights a day, leading to several cancellations.
Angry passengers say they were not informed ahead of time.
"Our flight was cancelled and there is no-one to answer us at the help desk. We don't know what to do now," a passenger in the southern city of Chennai told the ANI news agency.
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