Additively-manufactured flow restrictors are provided, as are methods for producing additively-manufactured flow restrictors. In various embodiments, the additively-manufactured flow restrictor includes a flowbody through which a flow path extends, a restricted orifice located in the flowbody and providing a predetermined resistance to fluid flowing along the flow path in a first flow direction, and a first internal perforated screen positioned in the flow path upstream of the restricted orifice taken in the first flow direction. The flowbody and the first internal perforated screen integrally formed as a single additively-manufactured piece utilizing, for example, Direct Metal Laser Sintering (DMLS) or another additive manufacturing process. In certain embodiments, the first internal perforated screen may include an endwall and a peripheral sidewall, which is integrally formed with the endwall and spaced from an inner circumferential surface of the flowbody by an annular clearance.