Nielsen originally joined the outfit when it was known as Team Lotus at the end of 2011 after several years at the Renault team.
It is not clear why he is leaving, but sources suggest that he is moving to another outfit. The Leafield-based team has confirmed he will stop working for them in January.
No replacement has yet been lined up, with Caterham using Nielsen's departure to evaluate a possible new structure to the sporting side of the operation.
Nielsen is an F1 stalwart, having previously worked at Arrows, Benetton/Renault, Tyrrell and the old Team Lotus, and his experience would be invaluable to any outfit on the grid.
Caterham endured a difficult 2012 campaign, when it failed to make the steps forward that it had hoped to.
However, it managed to hold on to its crucial 10th place in the constructors' championship after Vitaly Petrov finished 11th in the final race in Brazil to help his team overhaul rivals Marussia.