An air intake system for a work vehicle may generally include an intake duct defining a passageway for directing air in a flow direction through the system. The duct may also include a pre-cleaner slot defined between inner and outer surfaces of the duct and a support ledge extending circumferentially around at least a portion of an inner perimeter of the duct. The system may also include a pre-cleaner configured to be installed within the intake duct by inserting the pre-cleaner through the pre-cleaner slot in a direction extending generally perpendicular to the flow direction. In addition, the air intake system may include a cover configured to be coupled to the intake duct such that the cover extends over the pre-cleaner slot when the pre-cleaner is installed within the intake duct.