The men, aged 19 to 35, were arrested in central Madhya Pradesh state's Burhanpur district after locals complained they shouted pro-Pakistan slogans and lit firecrackers after the match on Sunday.
Similar arrests of four people were carried out on the same day by the Karnataka police in Kodagu district after the men allegedly set off firecrackers and raised slogans supporting the Pakistan cricket team.
"It's difficult to prove the sedition charge," senior police officer Burhanpur Parihar told The Indian Express, adding that the 15 men have now been charged with disturbing communal harmony instead.
Pakistan defeated reigning champions India by 180 runs at The Oval in London to win their maiden Champions Trophy title.
Earlier, Amnesty International slammed the arrests of the Indian men and demanded their immediate release.
"The arrests of at least 19 people for celebrating Pakistan cricket team's victory over India in the final of a major tournament is another worrying sign of the erosion of freedom of expression in India," the human rights organisation said in a statement.
Asmita Basu, Programmes Director of Amnesty International India, said "it is not a crime" to support Pakistan.
"Supporting a sporting team is a matter of individual choice and arresting someone for cheering a rival team clearly violates their right to freedom of expression," Basu said in a statement.
Last year, 21-year-old Ripon Chowdhry was arrested in India's Assam state for wearing a T-shirt bearing the name of former Pakistan captain Shahid Afridi.
In addition, around 60 students were arrested on sedition charges in India in 2014.
A Pakistani man was arrested in 2016 for waving an Indian flag after his idol, Indian captain Virat Kohli, scored a match-winning 90.
|Pakistan's win over India in the final was the first over their neighbours since 2014 [Andrew Boyers/Reuters]|