The incident happened at about 4:00 AM (0830 IST) at a meat market in the Mgbosimiri area of the city. Most of the victims were market women, said one trader, Agnes Tarila.
Local resident Arutere Utuama said: "As soon as I heard of the incident I ran to the market where I counted at least 10 bodies, including a husband and wife.
"Many others sustained various degrees of injuries."
"The motive for the killings is not clear yet as some of those killed may not have been the target of the gunmen," said force spokesman Nnamdi Omoni.
Rivers state and Port Harcourt have been hit by high levels of violent crime, including clashes between rival armed gangs and kidnapping for ransom.
The state has also long been a hotbed for politically linked violence, with Rivers a key prize to control because of its links to the lucrative oil industry.
Police said the attackers were suspected members of the Indigenous People of Biafra (IPOB), which wants a separate state for the Igbo people that dominate the southeast.
IPOB's push for secession has brought barely concealed religious and ethnic tensions to the boil.
Nigeria is a hotchpotch of hundreds of ethnic groups and languages but is broadly split into a Muslim-majority north and largely Christian south.
The Asaba market was mainly run by Hausas from the north.
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