The UK owner said the men were kidnapped after pirates boarded the 8,100-dwt Esther C (built 2008) south of the Gulf of Guinea on Thursday evening.
The ship was in international waters at the time of the raid.
The gunmen also took personal possessions.
Carisbrooke said: "The safety and well-being of these seafarers is the company's absolute priority and all possible steps to secure their return are being taken.
"The