The rights organisation expressed concern over the arrests, which it termed "another worrying sign of the erosion of freedom of expression in India".
Around 20 men were arrested in two separate regions of India for celebrating the Pakistani team's victory, according to Indian media reports.
The men were accused of spreading 'communal disharmony' and charged with sedition ─ an offence which is punishable with life imprisonment, Amnesty said.
Amnesty International India Programmes Director Asmita Basu termed the arrests "patently absurd", and said "the 19 men should be released immediately.
"Even if the arrested men had supported Pakistan, as the police claim, that is not a crime. 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.
According to Amnesty International, the First Information Report registered by the Madhya Pradesh police states: "[The accused] chanted 'Pakistan Zindabad' in support of the Pakistan cricket team…They celebrated Pakistan’s win by bursting crackers and distributing sweets…Their actions suggested that they were trying to conspire against the Indian government by supporting Pakistan in the cricket match…Because of them, there is an atmosphere of unrest in the village."
Basu called for repealing of the sedition law, which she said was "excessively broad and vague".
According to Amnesty, sedition is defined in the Indian Penal Code as any act or attempt "to bring into hatred or contempt, or…excite disaffection towards the government."
"The Supreme Court of India has ruled on multiple occasions that speech would amount to sedition only if it involved incitement to violence or public disorder," the Amnesty press release said.
The sedition law, Basu said, makes it easy to silence people who are legitimately exercising their right to freedom of expression".
"Nobody should have to go to prison merely because they are accused of causing offence. The sedition law has no place in a rights-respecting society, let alone one that has a proud tradition of pluralism and debate."
India's Supreme Court in a case in 2015 ruled that "Mere discussion or even advocacy of a particular cause howsoever unpopular is at the heart of [the right to freedom of expression]."