Striker Mulenga was forced off with a thigh problem in the 12th minute of Saturday's 3-1 defeat to Vitesse Arnhem, with tests revealing the full extent of the injury.
Former Swansea City winger Van der Gun, meanwhile, suffered a knee injury in training and will also not feature until 2014.
"Jacob Mulenga suffered a thigh injury on Saturday in the match against Vitesse," a statement on the club's website said.
"An MRI scan revealed that the Zambian has strained a muscle in his right thigh. This means that the attacker will not be action before the winter break.
"Cedric van der Gun is also not in action for the winter. The attacker was injured this week in training."
Mulenga and Van der Gun have scored a total of three goals for Utrecht so far this season, with the club sitting just three points clear of the relegation play-off zone.
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