The Republic of Ireland international hurt his left ankle in a challenge with Wolves defender Kevin Foley during the second half of the 2-1 win at Molineux on Saturday.
Cox was taken straight to the Queen's Medical Centre in Nottingham for preliminary X-Rays which revealed no obvious fracture, but he is still facing a spell on the sidelines.
He tweeted: "Morning yes I'm out for around 2 months but it feels better and better each day. I wanna be back ASAP to help the lads achieve our goal."
Cox, 25, joined Forest from West Brom for £2m in August and has scored five goals in 17 appearances for the club since then.