Jagtar Singh Johal, 30, from Dunbarton in Scotland has been in a Punjab jail since he was arrested earlier this month by the state's police for his alleged role in targeted killings in the state.
Local MP Martin Docherty-Hughes of the Scottish National Party (SNP) asked the UK Foreign Office what representations were being made to the Indian government on reports of his alleged "torture" in custody.
"We take any allegation of torture very seriously, as indeed would the Indian government," foreign office minister Rory Stewart told Mr Docherty-Hughes.
"It is completely unconstitutional, it is offensive to the British government and we will work very closely to investigate and, of course, we will take extreme action if a British citizen is being tortured," he said.
The minister of state in the Foreign Office stressed that the issue was being taken "very seriously" and that the deputy high commissioner of the UK had managed to gain access to hold a meeting with Johal.
The issue was raised in Parliament a day after British Prime Minister Theresa May was confronted by the BBC's Asian Network to comment on Johal's arrest in India.
"I am aware of the concern that has been expressed about Jagtar Singh Johal. Representatives from the Foreign Office have met with him and are pursuing the case and looking at this case and watching what is happening with concern and will take action necessary," she said.
Johal's MP, Mr Docherty-Hughes, has been campaigning for his freedom and has also written to Downing Street seeking a meeting for his UK-based family with the Prime Minister.
The Scottish-born Sikh was in Jalandhar with his family for his wedding last month when he was reportedly arrested by plainclothes police officials in the city.
Sikh Federation UK, a representative group leading a #FreeJaggiNow social media campaign, has quoted his lawyer Jaspal Singh Manjhpur as saying that Johal has been subjected to physical and mental "torture" in jail.
The All Party Parliamentary Group (APPG) for British Sikhs, led by Labour MP Preet Kaur Gill, had earlier written to UK foreign secretary Boris Johnson urging him to protect Johal's rights as a British citizen.
The Punjab government has claimed that Johal is among a group of suspects arrested on allegations of fanning communal disturbance in the state.