Trains are also suspended across Scotland from 7pm tonight with the fixture at Tynecastle kicking off at 7.45pm.
However, the Dark Blues have been informed by the Jambos that, as it stands, the game will survive the weather.
Posting on social media, Dundee said: “As things stand, Hearts are expecting tonight’s game to go ahead.
“Hearts will continue to closely monitor the situation throughout the day.
“Supporters making the journey to Tynecastle Park should allow extra time for travel and closely follow the advice of the Scottish Government and Transport Scotland.
“Please note that Scotrail has suspended its services from 7pm this evening.”
Dundee travel to Tynecastle for the first time this season after this fixture was re-arranged in November due to Hearts featuring in the League Cup semi-finals.
The Dark Blues sit seventh in the Premiership with the Jambos 14 points ahead in third.
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Hearts v Dundee: Premiership clash expected to be ON despite Storm Jocelyn turmoil
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