The Reds eased to a 3-0 win over Leeds in the Premier League on Sunday, but the game was marred by an injury to Elliott just before the hour mark.
Leeds defender Pascal Struijk was sent off for the challenge and Elliott was then treated on the pitch before being stretchered off.
The midfielder suffered a dislocated ankle and was taken to hospital, accompanied by Liverpool’s doctor.
Elliott has now been released and headed home, but he is due to undergo surgery.
The 18-year-old is likely to go under the knife on Tuesday after which he will then start to begin his recovery.
It is unclear how long Elliott will be out of action for.
The midfielder impressed last term on loan at Blackburn Rovers and had already begun to catch the eye at Anfield this term, with Jurgen Klopp handing him regular opportunities.