The blast brought down a tree onto a car, metres from a congealing puddle of blood where one of the victims had fallen, an AFP correspondent said.
It came hours after President Abdel Fattah al-Sisi, the former army chief who has battled militants since he overthrew the ruling Islamists last year, departed to New York for the UN General Assembly where he is expected to discuss militancy in the region.
Two lieutenant colonels died and six people were wounded by the improvised bomb, Egypts interior and health ministries said.
Police cordoned off the scene, in a crowded district in central Cairo along the Nile River, and scoured it with sniffer dogs for more bombs.
One of the officers, Mohamed Mahmud Abu Sarie, had testified in a court case on a prison break involving ousted Islamist president Mohamed Morsi in 2011, when he was an opposition leader jailed by former strongman Hosni Mubarak, a security official said.
It was unclear whether Abu Sarie was targeted for his role in the trial.
Militants have killed scores of policemen since Egypts military toppled Morsi in July 2013.
In the past, they have set off several bombs in succession to target first responders after the attack.
Two police bomb disposal experts were killed trying to defuse bombs outside the presidential palace in June, the last major attack in the capital before Sundays explosion.
The attack came days after Interior Minister Mohamed Ibrahim held a press conference to announc the killing and arrest of several Islamist militants.
"It is a cowardly act and a political message but it wont hinder the progress of the Egyptian people," Cairo governor Galal Said told AFP near the scene of explosion.
Some passersby gathered around chanting "the people demand the execution of the Brotherhood," referring to the now-banned Muslim Brotherhood movement of Morsi.
The Ajnad Misr militant group has claimed previous Cairo bombings, saying it was avenging more than 1,000 pro-Morsi protesters killed in street clashes with police after the Islamists ouster and detention.
Jihadists are mostly based in the restive Sinai peninsula, but have established cells in Cairo and the Nile Delta.
Police say they have disrupted many of the militant cells on the mainland but the elusive Sinai jihadists still regularly target policemen and soldiers in the mountainous and desert region bordering Israel and the Gaza Strip.
The main jihadist group, Ansar Beit al-Maqdis, last week claimed the killing of six policemen with a roadside bomb that destroyed their armoured vehicle.
The attack came days after another powerful roadside bomb killed 11 policemen in Sinai.
Protests in support of Morsi in Cairo and other Delta cities have started to give way to attacks on police amid a sweeping police crackdown that has netted thousands of Islamist activists.
The government says Morsis Muslim Brotherhood, designated a terrorist group after his overthrow, is responsible for the attacks. The group insists it is peaceful.
But with their scattered protests swiftly quashed by police, some
Brotherhood members and their allies are believed to have turned to attacking policemen, often using firebombs to target their vehicles.
The government has compared its battle against the militants with the mounting US-led campaign against Islamic State jihadists in Iraq, arguing the Islamists operate under one ideological umbrella.
The deadliest threat to the authorities comes from extreme Islamist militant groups like Ansar Beit al-Maqdis, which says it wants to implement Islamic law.
The group, which includes militants who had fought alongside jihadists in Syria, had bombed two police headquarters and tried to assassinate the interior minister last year using a suicide bomber.(*)