Recent studies have shown that runaway thermonuclear burning of material accreted onto neutron stars, i.e., Type I X-ray bursts, may affect the accretion disk. We investigate this by performing a detailed time-resolved spectral analysis of the superburst from 4U 1636-536 observed in 2001 with the Rossi X-Ray Timing Explorer. Superbursts are attributed to the thermonuclear burning of carbon, and are approximately 1000 times more energetic than the regular short Type I bursts. This allows us to study detailed spectra for over 11 ks, compared to, at most, 100 s for regular bursts. A feature is present in the superburst spectra around 6.4 keV that is well fit with an emission line and an absorption edge, suggestive of reflection of the superburst off the accretion disk. The line and edge parameters evolve over time: the edge energy decreases from 9.4 keV at the peak to 8.1 keV in the tail, and both features become weaker in the tail. This is only the second superburst for which this has been detected and shows that this behavior is present even without strong radius expansion. Furthermore, we find the persistent flux more than doubles during the superburst and returns to the pre-superburst value in the tail. The combination of reflection features and increased persistent emission indicates that the superburst had a strong impact on the inner accretion disk and it emphasizes that X-ray bursts provide a unique probe of accretion physics.