The 25-year-old suffered the injury in the 4-1 win at Craven Cottage after coming on as a substitute in the second half but appears optimistic the injury is not too severe.
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Cox, who has scored twice in five appearances for Sean O’Driscoll’s side since moving to the City Ground from West Brom in the summer, has been capped 17 times by Ireland, scoring three goals.
The former Reading and Swindon Town ace made his international debut in May 2011 and was selected by Giovanni Trapattoni to represent his country as part of the 23-man squad for Euro 2012.