Polyethylene is a promising low-cost alternative precursor material for carbon fiber production, but it has yet to show mechanical properties near or surpassing polyacrylonitrile-derived carbon fibers. The high molecular weight and order of ultra-high molecular weight polyethylene (UHMWPE) may offer a pathway to realizing this promise by enabling long-range graphitic structure formation and superior mechanical properties. The tension applied during the precursor stabilization process is crucial to maintaining the shape of the fibers during the conversion process, but no published study has yet probed the relationship between sulfonation tension and carbon fiber microstructure and mechanical properties. In this work, a logarithmic sweep of tensile stress was applied to UHMWPE fibers during the stabilization process followed by carbonization. Increasing tension significantly reduced fiber shrinkage, resulted in straighter fibers with less severe kink bands, and greatly improved the mechanical properties of the fibers. Raman spectroscopy and X-ray diffraction revealed that in all cases the carbon fibers were largely amorphous, but increasing tension resulted in increased size and alignment of the turbostratic crystallites with the fiber axis. Large voids were present in the sample fibers, so the Griffith-Irwin relation was employed to predict the potential ultimate tensile strength of the fibers with voids reduced to sizes comparable to commercially produced fibers. This work demonstrates the importance of tension applied during the stabilization of polyethylene fibers for carbon fiber production and establishes a framework for achieving high mechanical properties from these precursors.