Masih's lawyers said he was tortured into confessing to murder, in a case that has prompted concern among rights groups and the United Nations.
Aftab Bahadur was sentenced to death for killing three people in 1992 and human rights group Reprieve said two witnesses who said Bahadur was implicated under torture.
At the time, the death penalty could be passed on a 15 year old, but the minimum age was raised to 18 in 2000.
Testimony obtained by torture is also inadmissible.
"Aftab Bahadur was hanged at District Jail Lahore on Wednesday at 4.30 am," a jail official told on the condition of anonymity as he was not allowed to speak to the media on the issue.
"Before the hanging, he was crying and saying he was innocent."
The date of birth on Bahadur's birth certificate and national identity card, June 30, 1977, is not disputed by Pakistani police or the courts.
Read: Hours before his execution death row convict pens moving essay
"Pakistan proceeded with Mr Bahadur's execution despite his having been sentenced to death when he was a child - in violation of both international and Pakistani law," Reprieve said.
Aftab insisted he was innocent and said that when he was arrested, the police had asked for a Rs50,000 bribe and said they would let him go if he paid. As a plumber’s apprentice, Aftab said he could not pay.
Prime Minister Nawaz Sharif lifted the moratorium on the death penalty last year, a day after Pakistani Taliban gunmen attacked a school and killed 134 pupils and 19 adults. The killings put pressure on the government to do more to tackle the militant insurgency.
Read: SC adjourns Shafqat Hussain’s appeal hearing till tomorrow
In an essay written from jail and published a day before his hanging, Bahadur, a Christian, repeated his assertion that he was innocent.
"But I do not know whether that will make any difference," he wrote. "I have not given up hope, though the night is very dark ... It would perhaps have been better not to have to think of what the police did to try to get me to confess falsely to this crime."
In another incident, also at Kot Lakhpat Jail, a murder convict was hanged.
A duty officer at the jail confirmed to media that Tariq, alias, Tara was also executed for the murder of a man named Zahid.
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