Jamie George and Owen Farrell could both miss England's opening Six Nations match.
Owen Farrell could be out for up to three months after ankle surgery, which could keep him out of the Six Nations.
Jamie George will be out until the end of January with a knee injury.
The players were injured during the game.
England will play Scotland in the Six Nations on February 5.
Farrell, the fly-half, will be out for between 10 and 12 weeks, while George, the hooker, will be out for between eight and 10 weeks.
Both players were withdrawn from the England squad to face South Africa and replaced by Gloucester's Harry Elrington and Jack Singleton.
Farrell may be a doubt for England's second round fixture against Italy on Sunday, 13 February, but George will not require surgery, and may be in contention to make the first squad.
After initially testing positive for Covid-19, the playmaker was forced to miss the Test against Tonga, only to have the result confirmed as a false positive.
George was left out of the England's autumn internationals squad by head coach Eddie Jones, but fought his way back into it.
The return to full training of England and the British and Irish Lions has boosted the spirits of the team.
The 29-year-old has been out since the end of the Lions' tour to South Africa, but is available again for selection.
Marco Riccioni will have surgery on his right knee on Wednesday and will be out for the rest of the season.
The player sustained an injury playing for his country in the loss to Argentina.
