A pitch inspection was carried out at New Grosvenor during the afternoon.
The club tweeted that the game could not go ahead and a rescheduled date is yet to be announced.
Elsewhere, the Irish Cup fifth round replay at Inver Park between Larne and Lurgan Celtic has also been called off due to the weather.
The match is scheduled to be played at Inver Park in Larne on Tuesday 29 January.
Meanwhile, Stephen Douglas's late penalty fired Amateur League Kilmore Rec into the Irish Cup sixth round as they won at Tobermore United.
The spot-kick was awarded in the 88th minute at Fortwilliam Park following a foul by Tobermore centre back John Neill.
The two had come to a replay after the original tie - also at Fortwilliam Park - ended in a 2-2 stalemate.
Kilmore now go on to a last 16 clash with Institute.