The Championship side warned supporters in a statement to prepare for another alternative date as the condition of the waterlogged playing surface at The Valley was "becoming an increasing concern".
United were due to play their third round tie tomorrow, but it was postponed after a pitch inspection this morning.
It was rearranged for Wednesday, January 8, but with more rain forecast it is already in doubt.
Charlton's deputy head groundsman, Nathan Chapman, told the club's website: "We're in this predicament because the pitch hasn't had any sufficient drainage work done on it for the past 16 or 17 years.
"The drainage system is collapsed at one end which prevents any water from going through and as a result it just holds on the surface."
Charlton want to place a come over the pitch for a week to dry it out before they can work on the playing surface to make it playable.
It is the second time in three days a waterlogged pitch has thwarted United, after their New Year's Day trip to Newport County also fell victim to the wet weather.