The man died in hospital following the shooting near Havat Gilad, east of the Palestinian city of Nablus, the army said, without specifying if he was a settler.
Before being taken to hospital, the man was able to call for help on his phone, according to public radio, which aired the recording.
"I was shot near Havat Gilad," the man said, before collapsing.
The station said the man was in his 30s and lived in the settlement.
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About 400,000 Israelis live in settlements in the West Bank, a Palestinian territory occupied by Israel for 50 years.
The settlements are deemed illegal under international law and widely seen as a main obstacle to peace.
Fourteen Palestinians have been killed in unrest since President Donald Trump announced on December 6 that the United States was recognising Jerusalem as Israel's capital.
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