Preet Kaur Gill has demanded answers over the "targetting" of the men, known as the West Midlands Three, who were accused of being involved in a murder plot in India in 2009.
The Home Office certified an extradition request in December 2020, but an appeal to hand them over to Indian authorities was dismissed in September after a District Judge found that no case could be established.
Edgbaston MP Ms Gill, who is chair of the all party parliamentary group for British Sikhs, has demanded answers over the handling of the case.
She also called for the Home Office to push for the release of another British national, Jagtar Singh Johal, who has been held in an Indian jail without charge for more than four years.
Ms Gill said: "The case of the West Midlands Three is appalling. Having met with them, I've seen first-hand the unjust treatment which they have been subjected to.
"The targeting of innocent, British Sikhs has no place in our society.
"The Government must now answer serious questions concerning the treatment of these three British nationals who, if successfully extradited as the Home Secretary had wished, would face the death penalty.
"What is even more distressing for the Sikh community is that this is not the only case where the Government has actively allowed British Sikhs to be falsely accused of serious crimes by a foreign power.
"Jagtar Singh Johal has now been detained in India, facing the death penalty, for more than four years with only an alleged confession obtained under torture as evidence.
"In accordance with foreign office policy where an individual is arbitrarily detained, the UK Government must act and call for Jaggi's release. It is vital that the foreign secretary now makes this urgent request."
The case against the West Midlands Three – Piara Singh Gill, from Wolverhampton, and brothers Amritivir Singh Wahiwala and Gursharanvir Singh Wahiwala, from Coventry – collapsed when no further evidence was presented against them at court.
The British nationals were accused by Indian authorities of conspiring to murder Rulda Singh, who was shot dead in Patiala, Punjab, 12 years ago.
A West Midlands Police investigation in 2011 found no evidence of their involvement.
In the Commons on Tuesday, the Home Secretary was asked by Labour MP Taiwo Owatemi what evidence was used to justify their arrest.
Ms Patel told the MP she would like to discuss the matter with her personally.
A Government spokesperson 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.
“In-person consular visits in India are currently suspended due to the coronavirus pandemic. However, consular staff are having regular telephone calls with Mr Johal and have attended relevant court hearings."