The Leicester Tigers scrum-half was taken off early on in Rome, his evident pain souring what proved to be a commanding 46-15 win for England.
The Rugby Football Union (RFU) confirmed the 28 year-old had ruptured the medial collateral ligament in his left knee, bringing an end to his tournament.
Youngs will undergo a further assessment with a surgeon later this week, but the RFU said he could be sidelined for up to four months.
England coach Eddie Jones called up Saracens' Richard Wigglesworth as a replacement, with England facing Wales at Twickenham on Sunday (AEDT).
The news is also a huge blow to the Tigers, who are struggling in the bottom half of the Premiership.