Clashes broke out when the procession reached the village, with Palestinians hurling stones and Israeli soldiers firing tear gas grenades and rubber-coated bullets.
Five Palestinians were injured and a 16-year-old was in serious condition after being shot in the eye and the head with rubber-coated bullets, doctors at a nearby hospital said.
At the funeral, Rafik Husseini, an aide to Mahmoud Abbas, the Palestinian president, said Tuesday's shooting was "truly a crime against a child".
"The Israeli army, with its actions in Ni'lin and the rest of the West Bank, is trying to destroy any chance of peace and of a solution with two states living side-by-side," he said.
Salah Khawaja, a member of Ni'lin's Committee Against the Wall, said that Mussa died when soldiers fired live rounds towards a group of protesters running into Ni'lin village after being dispersed from the protest site by rubber-coated bullets.
According to Palestinian officials, an autopsy conducted by forensic doctors found that Mussa was shot by a live round.
Said Abu Ali, the governor of Ramallah, said that the autopsy indicated that Mussa was struck by a single bullet from an M16 assault rifle that entered his forehead and exited the back of his head.
Ali said Israel wanted to do a joint autopsy with the Palestinians either in Israel or in the West Bank, but Palestinian officials refused.
The Israeli military said it was investigating the boy's death.
The military also said in a statement that an initial inquiry indicated that youths were hurling "rocks in very large quantities".
Ahmed Saadat, a 10-year-old boy who saw the shooting, said he was with a group of children near a section of the barbed-wire fence on the edge of the village that had been cut by older boys earlier in the day.
Saadat said they threw rocks at soldiers who arrived in a military vehicle.
"A military Jeep came, and a soldier wearing a uniform got out and fired at us. He hit Ahmed directly in the head," he said.
Israeli border police said they would deploy forces better trained in riot control to deal with the protests in the future.
|Protests against the separation wall occur regularly around Ni'lin [AFP]
"This type of incident will not repeat itself," Superintendent Sharon Manor, a company commander in Israel's border police, said.
Manor also said that troops did not have permission to use live fire, but did not say whether the military thought that that was what killed the boy.
Al Jazeera's David Chater, reporting from Ni'lin, said that the use of live rounds is a controversial issue.
"Human rights groups have condemned its use, and say it is a breach of international law," he said.
"The growing anger against this wall, and the sheer number of protesters that continuously gather here has overwhelmed the police and the military, to an extent where they are losing control."
Fifteen people were also lightly injured by rubber-coated bullets during the demonstration in Ni'lin, which has in recent months become the site of regular demonstrations against the barrier.
Earlier this month, demonstrators in Ni'lin and other locations marked four years since the International Court of Justice issued a non-binding resolution calling for parts of the barrier inside the West Bank to be torn down and for a halt to construction there.
Israel has largely ignored the ruling.