"Doctors said Alex would be out for at least three weeks. There's a small chance he would be ready for (Champions League match at) Zilina on December 8," Kaprin told reporters.
The Brazil international was injured in a 1-1 draw against Rubin Kazan in a Russian premier league match on Monday.
The doctors said it was a different thigh injury to that he suffered last month, missing a 2-0 defeat by Chelsea in a Champions League match in Moscow on October 19.
Alex returned to Spartak's line-up for the Group F return fixture against Chelsea in London last week.
The Russians have also lost defender Sergei Parshyvlyuk for the rest of the year to a knee injury while fellow fullback Martin Stranzl and Brazilian striker Ari are both doubtful to face Marseille on November 23.
Spartak, who beat Marseille 1-0 in their Group F opener in September, are level on points with the French champions and the win for either club would almost assure each side a place in the knockout round along with group leaders Chelsea.
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