The incident happened on Monday night near Parrot Island, south of the Cross River state capital, Calabar.
"Information so far at our disposal is that the hoodlums came in four speedboats, attacked the vessel and abducted five men aboard," a senior police officer told AFP on condition of anonymity.
Dirk Steffen, a maritime security specialist at Risk Intelligence, added: "The vessel in question is the Cameroon- flagged general cargo ship Donna Simop.
"Information available to us suggests that four Cameroonian crew members and a Nigerian passenger were kidnapped," he said in an email exchange.
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Ship hijackings have become more frequent in Nigeria since President Muhammadu Buhari in 2015 announced he was winding down an amnesty to former militants in the oil-rich Niger delta region.
The number of pirate attacks off Nigeria rose from 14 in 2015 to 36 last year, according to the International Maritime Bureau.
Buhari's government has since resumed amnesty payments, causing a fall in rebel attacks on oil and gas infrastructure, but piracy is a constant threat in the Gulf of Guinea.
In February, seven Russian sailors and a Ukrainian national were kidnapped. They were rescued unhurt weeks later in March.