Security forces were defusing one makeshift bomb found at a street intersection near the presidential palace when a second device exploded, the Interior Ministry said.
They said the first bomb wounded three street cleaners, while the second exploded while a bomb squad was trying to defuse it, killing a police colonel and wounding three other people, the officials said. They spoke on condition of anonymity because they were not authorized to speak to the media.
Only two hours later a second Egyptian police officer was killed when another bomb went off, also as security forces tried to defuse it, state television and security sources said.
Monday's blast fells on the anniversary of the massive protests in which millions of Egyptians demanded that Islamist President Mohammed Morsi step down. The protests were followed by the military's ouster of Morsi on July 3 last year. The military chief at the time, Abdel-Fattah el-Sissi, was elected president in May for a four-year term.
The blast came days after the militant group Ajnad Misr, or Soldiers of Egypt, said it had planted a series of bombs in the same area to target security forces. It aborted the mission due to concerns that civilians would be hurt but was unable to remove the bombs and released a statement urging caution.
The group formally announced itself in January saying it would target the government after the army ousted elected Morsi of the Muslim Brotherhood last year.
Eight people were hurt in a series of explosions last week on Cairo's metro, the first attacks in the capital since Abdel Fattah al-Sisi became president this month.
Islamist militants have targeted police and soldiers with bomb attacks and shootings since Mursi's ousting. Thousands of Brotherhood supporters have been arrested, and hundreds more have been killed.
The Brotherhood denies any link to the violence.
Reuters and the Associated Press contributed to this report