The 24-year-old played the majority of the 1-0 win over Venezuela in a friendly in Florida on Friday.
The Argentina team posted on X saying Fernandez had "synovitis in his right knee."
Fernandez, who has scored three Premier League goals for seventh-placed Chelsea this season, is the club's latest midfielder to pick up an injury, with Cole Palmer, Dario Essugo and Andrey Santos also sidelined.
Argentina play Puerto Rico in another friendly on Tuesday, while Chelsea visit Nottingham Forest on October 18.