"It is a blow as Billy has had a good Six Nations but he is young and will be back," England head coach Stuart Lancaster said in the RFU statement.
"The encouraging thing is we have got Ben Morgan and other back rows such as Matt Kvesic and Tom Johnson, who are all competing hard for places."
England host Wales on March 9 aiming for their first Triple Crown since 2003 before facing Italy in Rome on March 15.
(Reporting by Tom Hayward; editing by Ken Ferris)
