Mend said it destroyed the Orubiri flow station on Tuesday with the help of another armed group, the Niger Delta Volunteer Force (NDVF).
It is the third attack in 48 hours on a Shell installation.
Mend has threatened to expand its so-called oil war to states outside Rivers state, saying that its next big attack would be on an offshore oil rig. It told foreign workers that they should abandon their posts.
"After Rivers, the hurricane will be heading to the neighbouring states in the Niger Delta," the group said in an email statement.
So far, pipelines, platforms and gas plants have all come under attack and numerous workers have been kidnapped for ransom.
Shell was not immediately available for comment.