Indian national Surjeet Singh alias Makhan Singh had completed his prison term on October 30, 2010 but he continues to be held in prison, Burney said in letters sent to President Asif Ali Zardari, Prime Minister Yousuf Raza Gilani and the Chief Justice of Pakistan's Supreme Court.
Another Indian national, Parmar, has been detained in Lahore's Kot Lakhpat Jail unlawfully without any charges or conviction since 2006, Burney said.
Parmar, an architect, became depressed after his father died in 2005 and went missing from home.
He reportedly travelled by train from his home city of Mumbai to Amritsar and later crossed over to Lahore, where he was arrested in 2006, Burney said.
Another prisoner, Karale, was being held in Kot Lakhpat Jail though the Lahore High Court had issued an order for his release on November 3 last year, Burney said.
"Despite providing documents verifying his identity, Karale has been illegally held in prison for almost five months," he said.
Burney, who served as the Human Rights Minister in a caretaker government in 2007-08, urged President Zardari and Prime Minister Gilani to direct the Interior Ministry to immediately release these three Indian nationals.
"The greater interest of human dignity and justice demands that the President and Prime Minister should release all foreign prisoners who have completed their jail terms," he said.