Israel has not confirmed the Bethelhem shooting.
Earlier on Wednesday, Saleh Karkur was killed in an exchange of gunfire with troops who had surrounded a house in the village of Saida, close to Tulkarem.
An Islamic Jihad official said Karkur belonged to the group.
Al Jazeera's correspondent Nour Odeh said that after the fire-fight, a bulldozer began to demolish the house without any forewarning, and recovered the body from the rubble.
An Israeli military spokesman acknowledged that troops were operating in Saida.
Large operation
Israeli forces also carried out raids in several other towns in the West Bank on Wednesday, including Qalqiya and Jenin.
So far, residents of these towns and surrounding villages have reported that Israeli forces have detained at least 12 Palestinians, Odeh said.
In Qalqiliya, the Israelis were involved in a large military operation, deploying in all its neighbourhoods to conduct random searches of residents' homes, Al Jazeera said.
Wednesday's death brings to 6,315 the number of people killed since the start of the second Palestinian uprising in September 2000, the vast majority of them Palestinians, according to a count by the AFP news agency.
Al Jazeera boycott
In separate development, Israel has decided to boycott Al Jazeera over what it called biased coverage of events in the Gaza Strip, according to an Israeli radio station.
The Israeli foreign ministry was reportedly sending a letter to Al Jazeera intimating its decision, but there has been no official confirmation.
Walid al-Umari, Al Jazeera's Palestine bureau chief, said the decision was part of a campaign against the channel, backed by Israel's foreign ministry.
He said: "A state that respects the freedom of expression or claims that it is democratic should not limit the movement of press teams.
"I dare any Israeli official to bring up what they call incitement or lies reported by Al Jazeera. What we reported were real facts on the ground."
Israeli officials will stop giving interviews to Al Jazeera's correspondents, who will also not be allowed to enter government departments, the radio station said.
In a statement released on Wednesday evening, Al Jazeera said it was very surprised to hear the Israeli radio broadcast, and that they had not received any formal communications from the Israeli government.
Al Jazeera reiterated that it has always endeavoured to cover the news in a fair, balanced and professional manner, and will continue to report from all over the world in accordance with the highest journalistic standards.