The side that beat Crystal Palace 3-0 in the third round on 8 February contained two unregistered players because of an administrative error.
They were poised to play Charlton on 8 March but the FA has reinstated Palace.
"Both the club staff and players are disappointed with the decision and apologise to the supporters for this mistake," stated the club website.
The original fixture at Crystal Palace was postponed because of an unplayable pitch before it eventually went ahead.
Reading were caught out because they fielded players who had not been registered prior to the original fixture date, making them ineligible.