Aftab Bahadur Masih's lawyer has said he was 15 at the time of sentencing, which would have meant he was too young to be condemned to death.
Pakistan rejects this and has claimed the man was 23 when he committed the crime.
Mr Masih, a Catholic, was hanged in Lahore early on Wednesday morning despite pleas for clemency from church leaders.
The Archbishop of Karachi, Joseph Coutts, wrote to the president, asking for the man's life to be saved.
It's claimed the evidence against Mr Masih was made under torture and two eyewitnesses have since retracted their statements.
International human rights group Reprieve said he was an "innocent man, arrested and tortured as a child".
Director Maya Foa said: "This is a truly shameful day for Pakistan's justice system. Aftab was subjected to almost every injustice conceivable.
"To the last, Pakistan refused even to grant his lawyers the few days needed to present evidence which would have proved his innocence.
"This is a travesty of justice, and tragedy for all those who knew Aftab."
Speaking to ucanews.com Cecil Chaudhry, executive director of the National Commission of Justice and Peace, a human rights body of the Catholic Church said: "It is unfortunate that authorities have gone ahead with the execution of Aftab Bahadur.
"Justice demands that if there is an iota of doubt, there should be an inquiry. In the Aftab Bahadur case, there was strong evidence to suggest that he was a juvenile at the time of his conviction.
"Two witnesses also retracted their statements and said Aftab was innocent."