"Members of the security services at Hizma spotted a man running in their direction with an object in his hand," a police statement said, referring to the checkpoint between Jerusalem and the occupied West Bank.
"They considered (him) an immediate danger to their lives and opened fire."
The attacker was a 20-year-old Jewish Israeli man from Jerusalem, the police said.
He was killed on the spot, they said, later publishing a picture of a short knife he was alleged to have been carrying.
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Palestinians often carry out similar attacks at Israeli checkpoints, with a number shot dead since a wave of attacks began in October 2015.
However there was no initial indication Tuesday's incident was linked to other attacks.
No similar attacks on security forces have been carried out by Israeli Jews since the wave of violence began.
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