Nonu, 34, was knocked out in an accidental high-impact collision with New Zealand compatriot Anthony Tuitavake in last weekend's 27-18 semi-final win over Montpellier.
He was immediately replaced having scored one of his team's tries and despite coming round, Toulon manager Bernard Laporte said that under current concussion protocols, Nonu has not had enough time to fully recover.
He will be replaced in Friday's final at Barcelona's Nou Camp stadium by powerful French centre Mathieu Bastareaud who will play alongside Maxime Mermoz.