Jagtar Singh Johal, from Dumbarton, was arrested in Punjab in November 2017 while celebrating his wedding.
A UN Working Group said his detention on terror offences was “arbitrary” and he should be released immediately.
The government said it had repeatedly raised concerns about the case.
In his letter to Boris Johnson, Sir Keir wrote: “When a UK national has been so gravely mistreated, with no legal basis, the UK government must act decisively to negotiate their release.”
He also asked why it appeared an official request had not been made, and asked when Mr Johal’s family could expect one.
Sir Keir said Labour would offer cross-party support to secure Mr Johal’s release.
Mr Johal’s brother Gurpreet Singh Johal, who was recently elected as a Labour councillor, said: “This intervention from Keir is highly crucial, coming from a former public prosecutor adds more weight.”
He added: “It’s time for the UK government to bring Jagtar home where he belongs.”
Mr Johal, 35, is accused of funding the purchase of weapons used to assassinate a number of right-wing Hindu religious and political leaders in the Punjab.
The Indian government has said his detention was based on “sufficient prosecutable evidence”.
It also said Mr Johal’s rights had been “duly honoured”.
A UK government spokesman said: “We have consistently raised our concerns about Mr Johal’s case with the government of India, including his allegations of torture and mistreatment and his right to a fair trial.
“The prime minister raised the case with his Indian counterpart Narendra Modi when they met in Delhi on 22 April.”