Champions League - Spartak star out of Chelsea clash
"Medical tests, which were done on Saturday, revealed a minor tear," Spartak coach Valery Karpin said.
"He'll need about seven to 10 days to recover."
The Brazil international was substituted at halftime in Friday's 3-0 league win over Alania Vladikavkaz shortly after scoring Spartak's second goal.
Alex's withdrawal has added to Spartak's mounting injury worries ahead of the top-of-the-table Group F clash against the English champions in Moscow.
The Muscovites could also miss leading striker, Alex's compatriot Welliton, who is yet to recover from a pulled thigh muscle, and Ireland winger Aiden McGeady, who did not play against Alania because of a leg injury.