Mr Sharif's convoy left from Jelhlum to Lahore where the incident took place at Lala Musa, some 225-km from Lahore.
"Hamid was standing on the road side when an elite squad vehicle of Nawaz convoy hit him and sped away. We rushed to rescue the boy but he died on the spot," Nadim, an eyewitness told reporters.
He said Hamid's father fainted seeing the crushed body of his son.
"We shifted Hamid's father to a nearby hospital where the doctors said he suffered a cardiac arrest," the eyewitness said.
Railways Minister Khawaja Saad Rafique said: "We regret the loss of a live. But the boy is the first martyr of our movement."
Mr Sharif's daughter Maryam Nawaz took to Twitter and expressed that the local leadership has been asked to reach out to the family of the boy.
"Extremely sad incident of death of a child being reported. Local leadership has been asked to reach out to & assist the family without delay," she tweeted.
Mr Sharif's son-in-law Captain Safdar termed the loss a "sacrifice for Pakistan."
"Millions of people rendered sacrifices during Pakistan's creation [too]...He is our child; if he joined [the rally meant] for Pakistan, [then] God bless him," he said.
Pakistan Muslim League-Nawaz or PML-N leader Khawaja Saad Rafique expressed grief on the child's death by the motorcade and said party's leaders will arrive at his house to condole the loss.
Meanwhile, Chairman of Pakistan People's Party or PPP Bilawal Bhutto Zardari condemned the incident, saying it was regrettable that vehicles in the former prime minister's convoy had hit and killed the boy.
Mr Sharif is leading a rally to Lahore as part of a campaign against his ouster by the Supreme Court in the Panama Papers case.