Elneny, 25, was injured during Arsenal's 4-1 home victory over West Ham United on Sunday, reported Efe.
"Further to assessments and scans on Sunday and Monday, we can confirm that Mo Elneny has sustained ligament damage to his left ankle," the English club said in a statement.
"We are hoping that Mo will be available for Arsenal again this season and we are keeping in regular contact with the Egyptian Football Association," the statement added.
Elneny is a member of Egypt's 2018 World Cup team.
Arsenal is set to host Atletico Madrid on Thursday at Emirates Stadium here.
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