They said a policeman on routine duty in the city's Manshiyah district “randomly” opened fire at a group of Israeli tourists visiting Pompey's Pillar, one of the city's Roman-era landmarks.
An Egyptian was killed and another wounded in the attack, said the officials.
The suspect has been detained and the wounded taken to hospital, they said.
The Israeli Foreign Ministry confirmed that two Israelis were killed along with their tour guide.
A video clip online showed the bodies of two males motionless on the ground with a pool of blood around one of them.
Two women were shouting in Hebrew as Egyptian policemen stood by. A third man, apparently wounded, sat on the ground next to one of the two bodies.
There have been incidents in the past when Egyptian policemen opened fire on Israelis or were killed in attacks on the border between Egypt and Israel.
In June, an Egyptian policeman on duty at the border killed three Israeli soldiers before he was killed.
In 2011, assailants who came from Sinai killed eight Israelis in an ambush north of the city of Eilat at the northern end of the Dead Sea's Gulf of Aqaba.
Pursuing Israeli soldiers killed seven of the attackers and five Egyptian policemen.
Egypt and Israel are bound by a peace treaty signed in 1979.
The neighbours have for years had what was known as a cold peace, but relations have deepened over the past decade with the exchange of intelligence on extremists and co-ordination on counter-terrorism policies.
They also co-operate on combating human trafficking into Israel from Sinai.
Sunday's attack comes after more than 300 Palestinians and 250 Israelis have been killed in the worst fighting to date between the militant Palestinian Hamas group and Israel.
An unknown number of Israelis have been taken hostage by Hamas after members of its armed wing launched a surprise attack on Friday.
Civilians and soldiers are believed to have been taken into the Gaza Strip, some of whom have been paraded by Hamas militants in video shared on social media.
Children and the elderly are thought to be among the hostages.
Israel has responded by launching air strikes on the besieged enclave.
At least 20 children have been killed so far, the Palestinian Health Ministry said.
Egypt, which borders Israel and Gaza, had in the past mediated truces that ended hostilities between Israel and Hamas. The last time it did that was in the summer of 2021.
Egyptian security officials say Cairo's efforts to end the latest fighting are hindered by ambitious Hamas demands, including a freeze by Israel on building new Jewish settlements in the West Bank and the release of thousands of Palestinians held in Israeli jails.
Israel's insistence on exacting a heavy price on the militant group before entering truce negotiations is another obstacle to the Egyptian peace effort, they said.