The Qatar-based news channel said Abu Aqleh, 51, was shot “deliberately” and “in cold blood” by Israeli troops. Another reporter was shot and wounded.
The Israeli military denied that its forces targeted journalists.
It was looking into “the possibility” that they “were hit by Palestinian gunmen” during an exchange of fire.
Israel’s Foreign Minister Yair Lapid described Abu Aqleh’s death as “sad” and said it had offered to carry out a joint investigation with the Palestinian Authority.
“Journalists must be protected in conflict zones and we all have a responsibility to get to the truth,” he added.
Qatar’s Assistant Foreign Minister Lolwah al-Khater said Abu Aqleh was shot “in the face” while wearing a press flak jacket and helmet.
The Palestinian health ministry confirmed Abu Aqleh’s death and said she had been rushed to hospital in critical condition after being shot.
Shereen Abu Aqleh was a prominent figure on Al Jazeera’s Arabic news service who had been covering the Israeli-Palestinian conflict for 15 years.
Al Jazeera journalist Nida Ibrahim said she was a “very well respected journalist” and that the news was “a shock to the journalists who have been working with her.”
A wave of attacks by Israeli Arabs and Palestinians in Israel in recent weeks has left 17 Israelis and two Ukrainians dead.
At least 26 Palestinians have been killed – including assailants shot dead while carrying out attacks, or militants and civilians killed during Israeli raids and confrontations in the West Bank.
Israeli operations have centred on the Jenin district, where four of the Palestinians who carried out attacks in Israel came from.
