We demonstrate the production of high-quality polymer opal fibers in an industrially-scalable process. These fibers exhibit structural color, based on the self-assembly of sub-micron core-shell particles, with a spectrum which is stretch-tunable across the visible region. The internal substructure and ordering of fibers, as inferred from variations in spectral bandwidth, is studied using dark-field microscopy. We employ a granular model to examine flow and shear forces during the extrusion process, and the effects on particle ordering. In both theory and experiment, a concentric zone of the fiber near the exposed surface develops particularly strong structural color. Such elastically-tuned structurally colored fibers are of interest for many applications.