Ramiro Funes Mori has been added to an Everton injury list that includes Seamus Coleman, James McCarthy and Morgan Schneiderlin.
Yannick Bolasie and Muhamed Besic are also sidelined – but are long-term absentees.
Mori was injured while playing for Argentina in their 2-0 defeat to Bolivia, and had to be stretchered off, and was replaced after just 36 minutes by Matias Caruzzo.
He had missed the 3-0 win over Colombia last Thursday due to suspension.
Everton boss Ronald Koeman must now wait to see if the 26-year-old former River Plate man will be back in time to face Liverpool in the Merseyside derby this weekend.
The Reds are, meanwhile, sweating on injuries sustained by a number of their players during this international break, including Thibaut Courtois and Adam Lallana.
A brief statement from Everton read: "Ramiro Funes Mori was forced from the field after just 36 minutes in Argentina’s 2-0 defeat to Bolivia on Tuesday evening.
"The defender departed the action on a stretcher after suffering an injury in the World Cup qualifier in La Paz.
"The former River Plate man has made 26 appearances for Everton this season."