The brazen attack brought fresh challenges for the country's army-backed interim government as it struggles to deal with a tense standoff with the Brotherhood that has left over 850 people dead since the security forces stormed two camps of supporters of ousted President Mohamed Morsi on August 14.
The supporters of Muslim Brotherhood have been staging demonstrations across the nation demanding reinstatement of Morsi - the country's first freely elected president - since his removal on July 3 by the army.
The policemen were in two buses which came under attack from men armed with rocket-propelled grenades in the Sinai Peninsula. At least three other policemen were injured in the attack, the report said.
The military recently intensified a crackdown against militants in Sinai, where attacks have surged since the fall of longtime ruler Hosni Mubarak in 2011.
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Earlier, the Muslim Brotherhood accused security forces of carrying out "cold-blooded" murder after at least 36 Islamists were killed while they tried to escape from a prison convoy.
But later the ministry said the prisoners died from the effects of inhaling tear gas, which was fired when the escaping detainees took a police officer hostage. He was freed, but was badly injured, the military's statement added.
"Thirty-six of the prisoners died of suffocation and crowding after tear gas was used to stop their escape," the Ministry said.
"They were reportedly assassinated in their truck with live ammunition and tear gas fired from windows."
"The murder of 35 detained anti-coup protesters affirms the intentional violence aimed at opponents of the coup, and the cold-blooded killing of which they are targets," it said in a statement in English.
The group said it "puts full criminal responsibility on leaders of the 3rd of July coup, beginning with Abdel-Fattah el-Sisi, (Egypt's army chief), and Minister of Interior Muhammad Ibrahim Kamel.