Icardi was injured towards the end of Friday’s 4-2 win in Brest.
PSG said in a statement that an examination confirmed Icardi’s injury.
“His return to squad training is estimated at between three and four weeks,” said the statement.
The injury is a setback for Icardi who has netted twice in the opening three rounds of the championship.
Apart from the match in Reims on Sunday, it is also set to rule him out of Argentina’s internationals in September.
Icardi could make his return for PSG in the Champions League in mid-September but for the moment he joins former Real Madrid defender Sergio Ramos in the infirmary.
The Spaniard, who is out with a calf injury, is due to make his first appearance for PSG after the international break.
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