Hussain, 24, was convicted of killing a child when he was just 14 and his supporters have long contended he was tortured into confessing.
He was hanged in a Karachi prison in the early hours of Tuesday morning, the rights group Reprieve said.
"Shafqat's execution speaks to all that is wrong with Pakistan's race to the gallows," said Maya Foa, director of the death penalty team at Reprieve.
"He faced a catalogue of injustice, sentenced to death while still a child after being tortured by the police until he produced a so-called confession."
Tried as an adult
At the time of the killing, Hussain was working as a security guard. Authorities charged him with involuntary manslaughter for kidnapping and killing a child.
Unable to afford legal counsel the state appointed him a defense lawyer, who, according to human rights groups, failed to provide any evidence or claim that Hussain was a juvenile.
This meant Hussain was tried as an adult in an anti-terrorism court.
Pakistan had a moratorium in place on death penalty. But the country lifted it following the attack on an Army Public School in Peshawar, which left at least 145 teachers and students dead. It was the deadliest act of terror in the country's history.
A social media campaign with the hashtag #SaveShafqat trended in Pakistan and protests were held in the capital to raise awareness about his case.
Hussain was initially due to be hanged on January 19, but under international pressure, Pakistan's Interior Minister Chaudhry Nisar called for a stay order.
Addressing parliament, the minister called for an investigation into the young man's age.
Two months later, another death warrant was issued for Hussain. Authorities ruled he was an adult at the time of his conviction.
"The government's decision to push ahead with the execution despite calls to halt it from across Pakistan and around the world seems to have been more a show of political power than anything to do with justice," Foa said.