The Hoops were due to face the league’s seventh-place side at 3pm on Saturday.
But Celtic Park is unable to host the fixture due to the affects of Storm Eowyn on the stadium.
Central Scotland was among many areas badly affected by winds of up to 100mph on Friday.
The Met Office issued a red weather alert signalling danger to life.
At 4pm on Friday, fans were warned the match could be called off – with extreme conditions preventing staff from assessing the damage at Parkhead until Saturday morning.
Now, five hours before kick-off, the game has officially been postponed.
A Celtic statement read: “Unfortunately, due to the stadium damage sustained yesterday we have been advised that we are unable to proceed with today’s match.
Celtic’s Scottish Premiership clash against Dundee has been postponed due to storm damage at Celtic Park. The match was originally scheduled for today, but Storm Éowyn’s extreme winds caused significant damage to the stadium, making it unsafe for the match to proceed .
Storm Éowyn made landfall on Friday, bringing winds of up to 100mph in some areas, including Drumalbin, Scotland. The storm has caused widespread disruption, including the death of a man in County Donegal, Republic of Ireland, and thousands of homes left without power .
Celtic has announced that the match will now take place on February 5. The club’s priority is the safety of its supporters, and they have been advised not to proceed with the match due to the stadium damage .
This isn’t the only Scottish football match affected by Storm Éowyn, as the Scottish League One match between Arbroath and Kelty Hearts was also called off on Friday due to storm damage at Gayfield Park .