The so-called Islamic State (IS) group said it was behind the attack.
The incident came hours after three foreign tourists were stabbed by suspected IS militants who stormed a hotel in the Red Sea resort of Hurghada on Friday.
Egypt is battling an insurgency largely based in the Sinai Peninsula which became more active after the overthrow of Islamist President Mohammed Morsi.
Hundreds of security force members and government personnel have been killed, with attacks creeping closer to the capital Cairo.
The instability has threatened Egypt's important tourism industry.
Those injured in the attack in Hurghada - two Austrians and a Swede - are said to be in a stable condition.
Security forces shot dead one of the attackers and wounded the other.
Both were armed with knives and reports say they raised the IS flag.
"Everything happened so quickly," said the wounded Swedish tourist, Sammie Olovsson. "I thought I would bleed to death."
Egypt's ambassador to the UK, Nasser Kamel, said his country was no less safe than other countries, adding there was no reason to stop visiting.
"We are facing the exact same threat in Paris, unfortunately in London, all over the world," he said.
IS has an affiliate based in the Sinai Peninsula, known as Sinai Province.
It said it was behind the downing of a Russian jet last year that killed 224 people.
Gunmen have killed two Egyptian police in the city of Giza, officials said.