The Tottenham midfielder was stretchered off during the second half of Arsenal's 1-0 victory at the Emirates.
And a short statement released on the Spurs website confirmed the summer signing did not suffer ligament damage or a broken bone in a collision with Santi Cazorla.
It read: "Capoue was immediately taken to hospital to consult with a foot and ankle specialist.
"Early indications suggest the France international will be unavailable for a period of four weeks."
Capoue is now likely to miss Premier League games against Norwich, Cardiff and Chelsea, a Capital One Cup trip to Aston Villa and Spurs' Europa League group opener against Tromso.