Interior minister Ivica Dacic said the assailant, who has not been identified, fired a bolt at the officer, who “used a weapon in self-defence to shoot the attacker”.
The policeman was conscious when he was transported to the main emergency hospital in the capital Belgrade, where medics will operate to remove the bolt.
He is in a life-threatening condition, according to Serbian news agency Tanjug.
“This is a terrorist attack against Serbia,” Mr Dacic said in the statement cited by Tanjug.
Several people believed to have been linked to the incident have been arrested.
“There are some indications that they are already known to security services and we are talking about the Wahhabi organisation, but that is not confirmed,” Mr Dadic said, referring to a strict school of Islam.
The policeman was in a guard house and the attacker had approached him several times asking him where a museum was.
He carried a bag from which at one point he took the crossbow and shot the guard, Mr Dacic said, with the guard firing back at him several times.
Mr Dacic told reporters “we are still talking about possible motives” but “there are now all indications that the motives relate to terrorism”.
He added: “Because there is no other motive why someone would attack a gendarme outside the Israeli embassy.”
A spokesman with the Israeli Ministry of Foreign Affairs said “today there was an attempted terrorist attack in the vicinity of the Israeli embassy in Belgrade”.
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The spokesman added the embassy is closed and no employee was hurt.
Israel’s embassy, which is guarded by an elite police unit with officers armed with automatic weapons, is not far from the US embassy in an upscale Belgrade district.
Serbia has maintained close relations with Israel during the war in Gaza.
