The summer signing from Toulouse was stretchered off after 75 minutes after clashing with Santi Cazorla in the north London derby fixture on Sunday - with Olivier Giroud's first-half effort sealing the victory for the Gunners.
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Capoue was immediately taken to hospital to consult with a foot and ankle specialist, and Spurs have confirmed that "early indications suggest the France international will be unavailable for a period of four weeks".
The 25-year-old has featured in all three of Andre Villas-Boas' side's Premier League games thus far this season, making his first start in the league in the 1-0 win over Swansea City on August 25.
Capoue's spell on the sidelines will likely see him miss Premier League fixtures against Norwich, Cardiff and Chelsea, while he'll also be unavailable for the Capital One Cup tie against Aston Villa and the Europa League group stage opener against Tromso.