The association said in a statement on their official website they had received a letter from the world governing body rejecting their request to find a "safe and secure venue".
A FIFA security delegation visited the Egyptian capital after asking for safety guarantees from Egypt.
The GFA said fans would be allowed into the Air Defence Stadium.
The statement on www.ghanafa.org read: "FIFA says the World Cup play-off between Egypt and Ghana will go ahead in Cairo despite a request for next month's game be moved to a neutral venue.
"The Ghana Football Association expressed concern at the security situation in the Egyptian capital, as it urged world football's governing body to find 'a safe and secure venue' for the November 19 return leg.
"But FIFA in response to the GFA on Wednesday confirmed Cairo as the venue for the second-leg match following a recent visit by its security inspection delegation after writing to Egypt to provide the sport body with guarantees on the security situation for next month's tie."
"FIFA added that the decision of CAF (Confederation of African Football) to host the Champions League final on 10 November at the Air Defence Stadium shows that 'the current situation in Egypt has turned back to normal', the letter from the world governing body read.
"The decision means football fans will be allowed into the Air Defence Stadium for the game."
Ghana will take a 6-1 lead into the second leg after a thumping first-leg win in Kumasi.