Egypt is facing an insurgency based in North Sinai that has killed hundreds of soldiers and police since the army toppled Islamist president Mohamed Mursi in 2013 following mass protests against his rule.
Most attacks have taken place in the Sinai Peninsula, a remote but strategic region bordering Gaza, Israel and the Suez Canal, but smaller-scale bombings have become increasingly common in Cairo and other cities.
A bomb explosion on a bridge leading to the upscale Cairo district of Zamalek, which hosts several embassies, killed one policeman, security sources said. Two more officers and a civilian were injured, they said.
The force of the explosion, which the sources said was planted in or near a car, left a crater in the ground.
On Saturday, two bombs exploded near a police station in the residential Imbaba district across the Nile River from Zamalek, causing no casualties.
Sunday's bombing was claimed on Twitter by Ajnad Misr, a militant group that emerged in January 2014 and has targeted security forces in and around Cairo.
"God has enabled our brave soldiers to plant an IED where the criminal (security) services were gathered on the bridge," Ajnad Misr's media wing said.
In a separate incident, the founder and leader of Ajnad Misr was killed by security forces early on Sunday, security sources said.
Hamam Mohamed Attia of Ajnad Misr was shot dead during a firefight around 1 a.m. (2300 GMT) at an apartment in Giza, a suburb of the capital, the security sources said.
There was no immediate comment on Attia's death from Ajnad Misr, and the group did not signal that the bombing was in retaliation for his killing.
Security sources say the group is guided by a conservative Salafist Islamist ideology but it is not believed to have ties to al Qaeda or the Egyptian affiliate of Islamic State, Sinai Province.
Sinai Province, which changed its name from Ansar Bayt al-Maqdis after pledging allegiance to Islamic State, has claimed responsibility for much of the violence wracking the Sinai Peninsula, while Ajnad has focused more on the greater Cairo area.
The last attack claimed by Ajnad Misr was a March 28 bombing near the gates of Cairo University that wounded four police officers and two civilians.
Security sources also said that unidentified gunmen attacked Sheikh Zuweid police station in North Sinai, but the militants escaped without injury to either side.
