Diawara, 33, suffered a "serious sprain with a tear of the back cruciate ligament in his right knee", the club said on their website.
Diawara was already scheduled to miss Wednesday's Champions League quarter-final first leg against Bayern Munich because of suspension, but had been expected to play the return in Germany on April 3.
Senegal, dumped out of the last African Nations Cup in the first round with three defeats, have two World Cup qualification matches scheduled for June.
Marseille, who drew 1-1 with Nice, are eighth in Ligue 1.
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