The attacker, a resident of east Jerusalem, entered a border guard post and wounded the two before being shot dead, they said.
One of the guards was seriously injured, the other more lightly, police added.
Family members named the dead assailant as 25-year-old Ibrahim Matar from the Jabal Mukaber area of east Jerusalem.
Police spokesman Micky Rosenfeld said security forces later raided his home and that four people were arrested. Family members said they included Matar's father.
A wave of violence that broke out in October 2015 has killed 255 Palestinians, 40 Israelis, two Americans, one Jordanian, an Eritrean and a Sudanese national, according to an AFP count.
Most of the Palestinians who lost their lives were carrying out knife, gun or car-ramming attacks, according to Israeli authorities.
Others were killed during protests, in clashes or Israeli air raids on Gaza.
Violence has greatly subsided in recent months, despite sporadic attacks.
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