The ministry in a statement said the attacks on security forces are common in Egypt’s northern Sinai, where the country is battling an Islamist insurgency, but targeted assaults in Cairo are rare.
The ministry said the shooting comes amid a campaign by militants to spread violence to the country’s mainland.
It said the militants drove by and shot down police stationed at an intersection of the ring road, a busy Cairo expressway, in the city’s eastern neighbourhood of Nasr City.
No group has claimed responsibility for the attack.
It comes just weeks after two Islamic State suicide bombers killed at least 45 in deadly church bombings in Alexandria and Tanta, one of the bloodiest attacks the country has experienced in years.
The attacks also comes three days after Pope Francis warned against religious fanaticism on Saturday, wrapping up a brief trip to Cairo.
He urged Muslim leaders to unite against violence by Islamic militants threatening to rid the Middle East of its ancient Christian communities.
The Pontiff blessed Egypt as one of the earliest nations to embrace Christianity and repeated his plea for tolerance.
“True faith leads us to protect the rights of others with the same zeal and enthusiasm with which we defend our own,” he told the crowd in the heavily guarded arena.
“The only fanaticism believers can have is that of charity. Any other fanaticism does not come from God and is not pleasing to him,” he said in his homily.
In a series of speeches during his two-day stay, the pope has delivered his bluntest denunciations yet against religious violence, and has appeared to endorse Egyptian President Abdel-Fattah al-Sisi’s campaign against Islamist militants.
However, he nuanced his message by lamenting the rise of “demagogic forms of populism”, a possible reference to right-wing nationalist parties in Europe pushing anti-immigrant and anti-Muslim agendas.
He also defended human rights, which non-governmental organisations have accused Sisi’s administration of abusing.
“History does not forgive those who preach justice, but then practice injustice,” he said in a speech on Friday, sharing the stage with Sisi, who warmly applauded his words.
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