A system to continuously produce fully carbonized or graphitized carbon fibers using microwave-assisted plasma (MAP) processing comprises an elongated chamber in which a microwave plasma is excited in a selected gas atmosphere. Fiber is drawn continuously through the chamber, entering and exiting through openings designed to minimize in-leakage of air. There is a gradient of microwave power within the chamber with generally higher power near where the fiber exits and lower power near where the fiber enters. Polyacrylonitrile (PAN), pitch, or any other suitable organic/polymeric precursor fibers can be used as a feedstock for the inventive system. Oxidized or partially oxidized PAN or pitch or other polymeric fiber precursors are run continuously through a MAP reactor in an inert, non-oxidizing atmosphere to heat the fibers, drive off the unwanted elements such as oxygen, nitrogen, and hydrogen, and produce carbon or graphite fibers faster than conventionally produced carbon fibers.