The Colombia international does not need surgery but will likely miss 10 matches in Liverpool's packed schedule ahead of the World Cup, which starts on November 20th.
The Reds will hope to have Diaz back for their visit to Aston Villa on December 26th in their first match after the World Cup, which Colombia have not qualified for.
Liverpool's England defender Trent Alexander-Arnold (24) also sustained ankle damage in Sunday's match and manager Jurgen Klopp said after the match that both injuries did not look good.
"Lucho (Diaz) we had to change before (halftime). (It's) something with the knee, not good," he said.
Diaz has made 12 appearances in all competitions so far this season, scoring four goals with three assists.
Liverpool have struggled this season and are 10th in the table with 10 points after eight matches. They travel to Rangers in Group A of the Champions League on Wednesday.
