The Palestinian Health Ministry and the Palestinian Red Crescent identified the man as Zakaria Qatusa, 44, from the town of Deir Qadis, about 20 kilometres northwest of the site of the shooting Tuesday evening in the West Bank town of Al-Ram, which abuts the wall.
Israeli police didn't immediately respond to queries about the shooting.
The funeral for the man was held on Wednesday.
Khalid Qatusa, his brother, said that he was a father of four who was crossing the wall in order to work in Israel.
"He was forced to resort to this method as there was no other opportunity to meet the needs of his household and live a dignified life. This was the only way," he said.
"He was neither an aggressor nor a threat."
An increasing number of Palestinians from the occupied West Bank have attempted to enter Israel illegally to work in recent years.
Before the Israel-Hamas war, tens of thousands of Palestinians held permits to work in Israel, but access was sharply restricted after the attack by Hamas-led militants on southern Israel on October 7, 2023.
Since then, unemployment has surged amid a deep economic slowdown and a shortage of jobs in the occupied West Bank.
Other shootings have taken place at the same location, separating the West Bank town of Al-Ram from Beit Hanina, an east Jerusalem neighbourhood.
Also on Wednesday, a Palestinian teenager was killed in a clash with Israeli settlers in the northern West Bank village of Al-Lubban al-Sharqiya. The Ramallah-based Palestinian Health Ministry identified the victim as 16-year-old Youssef Kaabneh.
The Israeli military said soldiers and police officers entered the area in response to reports that livestock from an Israeli outpost was stolen. They said they worked to disperse a violent riot and were investigating the incident.
Family members said settlers and Israeli soldiers descended on the Bedouin community and that Kaabneh was shot during a confrontation involving a sheep herd.
As Israeli settlers expand their presence and outposts, livestock theft has been a major source of conflict between Israelis and Palestinians this year.
"Our lives have become a living hell. Settlers can now enter any house or farm and confiscate whatever they want, as if we are spoils of war," said Ismail Owais, a 60-year-old resident of the village.
According to the UN Office for the Coordination of Humanitarian Affairs, Israeli forces or settlers killed at least 47 Palestinians in the occupied West Bank this year as of May 11.
Several, like Kaabneh, have been teenagers.
