Residents reported hearing explosions and seeing a large plume of smoke rising over the city.
Bassie Inyang, a police official in the city, said police and bomb disposal experts at both locations had no reports of casualties.
Both blasts appeared to hit residential compounds when most workers would be in their offices.
Much of the Niger Delta oil-pumping infrastructure is sited away from highly-populated areas like Port Harcourt, making it unlikely Monday's blast would result in large reductions in oil production.
The group is currently holding four foreign oil workers, three Italians and one Lebanese, who were taken hostage on December 7.
It also detonated two car bombs earlier this year, one at a military barracks in Port Harcourt and another near an oil refinery in Warri.
Attacks on pipelines and oil facilities have cut the West African country's usual daily output of 2.5 million barrels by about a quarter this year.