Massive stars at redshifts z ≳ 6 are predicted to have played a pivotal role in cosmological reionization as luminous sources of ultraviolet (UV) photons. However, the remnants of these massive stars could be equally important as X-ray-luminous (LX ∼ 1038 erg s -1) high-mass X-ray binaries (HMXBs). Because the absorption cross section of neutral hydrogen decreases sharply with photon energy (σ∝E -3), X-rays can escape more freely than UV photons from the star-forming regions in which they are produced, allowing HMXBs to make a potentially significant contribution to the ionizing X-ray background during reionization. In this paper, we explore the ionizing power of HMXBs at redshifts z ≳ 6 using a Monte Carlo model for a coeval stellar population of main-sequence stars and HMXBs. Using the archetypal Galactic HMXB Cygnus X-1 as our template, we propose a composite HMXB spectral energy distribution consisting of blackbody and power-law components, whose contributions depend on the accretion state of the system. We determine the time-dependent ionizing power of a combined population of UV-luminous stars and X-ray-luminous HMXBs and deduce fitting formulae for the boost in the population's ionizing power arising from HMXBs; these fits allow for simple implementation of HMXB feedback in numerical simulations. Based on this analysis, we estimate the contribution of high-redshift HMXBs to the present-day soft X-ray background, and we show that it is a factor of ∼100-1000 smaller than the observed limit. Finally, we discuss the implications of our results for the role of HMXBs in reionization and in high-redshift galaxy formation. © 2013. The American Astronomical Society. All rights reserved.