The 27-year-old was substituted in the 87th minute of Sunday's 3-1 Premier League win over Manchester City after picking up the knock in a challenge with Fernandinho.
Salah met up with Egypt in Cairo on Tuesday for tests on the injury.
"The injury needs a period of treatment to recover," said an Egypt statement.
Salah missed Liverpool's draw against Manchester United in October after a tackle by Leicester's Hamza Choudhury injured the same joint.
Club manager Jurgen Klopp, who had been angered by Choudhury's tackle in Liverpool's 2-1 win, said before Salah's latest setback that his joint top-scorer was still feeling the effects of that initial knock.