The Mend statement described the target of the attack as a "major trunk pipeline" in southern Rivers State.
"We flanked them in a counter-attack and killed in close combat all the drunken soldiers numbering 11 ... before using dynamite to sink the gunboat with its dead occupants," the statement said.
Shell was not immediately available for comment.
Nigeria is Africa's biggest oil producer and continues to battle fighters from Mend who have sabotaged several supply pipelines owned by Shell and other oil operators in the region.
Mend emerged in early 2006 as the leading group calling for a greater share of Nigeria's oil revenue.