A system for cleaning an air intake screen of a work vehicle may include an engine air intake assembly having an air intake screen through which an airflow is directed for subsequent delivery to an engine of a work vehicle. The system may further include a nozzle provided in operative association with the engine air intake assembly and directed towards the air intake screen. Additionally, the system may include a pressurized fluid source configured to supply pressurized fluid to the nozzle. The pressurized fluid received by the nozzle is expelled from the nozzle and directed through the air intake screen.