The Stade Francais lock was taken to hospital following the clash, although it was expected that he would be fit to resume France's campaign this weekend.
However, Pape, who captained his country for the first time at the Stadio Olimpico, has been ruled out of the match by France coach Philippe Saint-Andre.
"I can tell already that Pascal Pape will be absent against Wales. He suffers from sciatica," he told reporters.
Jocelino Suta is expected to replace Pape in the starting side.