The family of Rayan Suleiman said he had no health problems and he was “shrieking in fear” at sight of the Israeli forces.
The US State Department has called for an investigation.
His father Yasser Suleiman said Rayan tried to run away when the soldiers said they wanted to arrest his brothers and was briefly chased by the soldiers.
He said Rayan was vomiting blood in the car after collapsing and was pronounced dead at the hospital.
“He was martyred from the fear of them,” the father told Palestine TV.
Mohammed Suleiman, a 22-year-old cousin, said his parents shouted, “come here,” to calm him down. He said after the soldiers left, the boy collapsed.
A medical official who inspected the body told Reuters that it bore no sign of physical trauma and that the death appeared consistent with heart failure.
The Israeli army called the death a tragedy and said its soldiers were not to blame.
Military spokesman Lt Col Richard Hecht said a senior officer on the scene went to the house after spotting one of the stone throwers on a balcony and told the father to make the children stop throwing stones at motorists.
He said the officer spoke in a “very calm manner” and left, AP reported.
“There was no violence, no entry into the house,” Lt Col Hecht said.
An Israeli military spokesman said troops were in the vicinity at the time to search for Palestinians suspected of fleeing into the village after throwing rocks at motorists.
“An initial inquiry shows no connection between the searches conducted by the Israel Defence Forces in the area and the tragic death of the child,” the spokesman said.
Palestinian residents said there was no stone-throwing at the time. The military spokesman added that “the details of the incident are under review”.
The Palestinian Foreign Ministry condemned the incident as “an ugly crime” by Israel.
The incident added to the rising tensions in the occupied West Bank, where Israeli troops have been conducting daily arrest raids that have frequently escalated into deadly violence in recent months.
Palestinian village boys were seen throwing stones at cars driving on a highway near the Israeli settlement of Tekoa, close to Bethlehem.
Later, relatives said that soldiers banged on the door and wanted to arrest Rayan’s older brothers for alleged stone throwing.
US calls for 'thorough' investigation
The US State Department is calling on Israel to open a “thorough” investigation into the death.
State Department deputy spokesman Vedant Patel said the US was “heartbroken to learn of the death of an innocent Palestinian child”.
“We support a thorough and immediate investigation into the circumstances surrounding the child’s death,” Mr Patel said.
Palestinians and human rights groups say the army is incapable of investigating wrongdoing by its forces and that soldiers are rarely held accountable.
The boy was scheduled to be buried on Friday. The funeral comes at a time of rising violence in the West Bank.
On Wednesday, four Palestinians were killed and 44 wounded during an Israeli military raid in the northern West Bank town of Jenin. It was the deadliest episode since Israel launched its crackdown earlier this year.
Israel has been conducting nightly arrest raids, primarily in the northern West Bank, since a series of deadly Palestinian attacks in Israel last spring.
Israel says most of the dead have been wanted militants who opened fire, or youths who threw firebombs or stones at soldiers entering their neighbourhoods.
But human rights groups say several civilians who were not involved in any violence have also died.