Ruth Patterson, who made the comment on Facebook, is a member of the Belfast council and of the Democratic Unionist Party, the Belfast Telegraph reported. She was responding to a fictitious account of an attack on the upcoming parade that said leading members of the Sinn Fein Party were killed.
"Who cares how we would be judged, we would have done a great service to Northern Ireland and the world," Patterson wrote in a comment.
She has since apologized.
The Police Service of Northern Ireland said Patterson faces charges of violating laws the ban encouraging criminal behavior.
Her party called the arrest "sensationalist," saying she could have simply been questioned.
The march, scheduled for later this month in Castlederg, is being held to honor two members of the Irish Republican Army. They were killed 30 years ago when a bomb they intended to plant in Castlederg exploded prematurely.
The march organizers voluntarily rerouted it and the Parades Commission made additional changes. But unionists have called on the Northern Ireland secretary to ban it.