Suffolk Police were called at 23:45 GMT to reports of an incident in the boiler room of the Manhattan Bridge ship while it was docking at the Trinity Terminal.
One person was killed and another taken to hospital. The death is not being treated as suspicious.
There will be a joint investigation between the police and the Maritime and Coastguard Agency.
People who live nearby described hearing a loud explosion.
On the port's website, the Manhattan Bridge is reported as being a Japanese ship run by "K" Line which had last docked at Rotterdam and was due to head to Hamburg.
It appears to have arrived in Felixstowe at 23:12 on Thursday.
A port spokesman said they would not be making any further comment at this time.
A person has died in what people have described as an "explosion" on board a ship at the Port of Felixstowe.