"Kayser sustained a partial ligament rupture in the right knee and will be sidelined for up to six weeks," his club side Clermont said on their website (www.asm-rugby.com) on Saturday.
The player is a regular for France who are level with Ireland on four points at the top of the table.
France play their third game of the Six Nations season in Wales on Friday.
(Reporting by Gregory Blachier; editing by Tony Jimenez)
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