Similar celebrations have roused the ire of Indian politicians in the past, as the nuclear-armed neighbours are at loggerheads over the Himalayan territory of Kashmir, which both claim in its entirety, although each controls only a part.
Pakistan resoundingly beat India at the Twenty20 World Cup on Sunday, for its first cricket win against its bigger neighbour in such a match, triggering celebrations at home and in Muslim-majority Kashmir.
"Those celebrating Pakistan's victory will face sedition," the office of Yogi Adityanath, the chief minister of India's northern state of Uttar Pradesh, said on Twitter, with an accompanying screenshot of a news report.
The offence, if proved, carries a maximum penalty of life imprisonment.
Adityanath's office had ordered state police to take action depending on the circumstances of each case, said state information official Navneet Sehgal, adding that police would decide on the charges based on their investigations.
Posts on social media hailing Sunday's victory by Pakistan were made by three Kashmiri students at a college in the state's city of Agra, according to a police complaint on Tuesday that was reviewed by Reuters.
The three were arrested late on Wednesday, said city police official Saurabh Singh, on charges of promoting enmity between different groups and causing public alarms.
In the restive Kashmir valley, where some resident chafe at Indian control, authorities said police had received complaints over celebrations at two medical colleges after Pakistan's victory.
Authorities said six people had been detained in adjoining Jammu, where social media posts showed more than two dozen people celebrating after India's loss.
"The investigation is going on," said local official Anuradha Gupta.