An unidentified civilian was also killed in Tuesday's attack, which occurred near Bayelsa state, Leadership Newspapers reported.
Authorities confirmed the victims were on an official escort of an oil barge owned by Sterling Global Services Oil Co.
The destination of the barge is unknown, Leadership Newspapers said.
A witness said the gun battle between the pirates and military personnel lasted for hours.
An official confirmed one of the three unidentified gunmen was also killed in the battle.
Witnesses said five boats pursued the pirates after the attack, Leadership Newspapers reported.