The first blast killed one officer and injured three others. The second device blew up as security forces tried to defuse it, killing the other officer.
The attack coincides with the first anniversary of the mass opposition protests that led to the military overthrowing President Muhammad Morsi.
Cairo's security chief said that the head of the bomb-disposal department, Gen Alaa Abdel Zaher, was among those injured by Monday's explosions.
Meanwhile, the civil defense deputy chief said security forces were currently defusing two other bombs found outside the presidential palace.
A source inside the presidential palace said President Abdel Fattah al-Sisi's schedule had not been changed following the blasts.
Armed groups have targeted police and soldiers with bomb attacks and shootings since Morsi's ousting. Thousands of Brotherhood supporters have been arrested, and hundreds more have been killed.
The Brotherhood denies any link to the violence.
RA/NJF