We present a generalized analytic formalism for the inverse Compton X-ray emission from hydrogen-poor supernovae and apply this framework to SN 2011fe using Swift X-Ray Telescope (XRT), UVOT, and Chandra observations. We characterize the optical properties of SN 2011fe in the Swift bands and find them to be broadly consistent with a "normal" SN Ia, however, no X-ray source is detected by either XRT or Chandra. We constrain the progenitor system mass-loss rate M < 2 x 10 super(-9) M sub(odot) yr super(-1) (3sigma c.l.) for wind velocity v sub(w), = 100km s super(-1). Our result rules out symbiotic binary progenitors for SN 2011fe and argues against Roche lobe overflowing subgiants and main-sequence secondary stars if gap 1% of the transferred mass is lost at the Lagrangian points. Regardless of the density profile, the X-ray non-detections are suggestive of a clean environment (n sub(CSM) < 150 cm super(-3)) for 2 x 10 super(15) lap R lap 5 x 10 super(16) cm around the progenitor site. This is either consistent with the bulk of material being confined within the binary system or with a significant delay between mass loss and supernova explosion. We furthermore combine X-ray and radio limits from Chomiuk et al. to constrain the post-shock energy density in magnetic fields. Finally, we searched for the shock breakout pulse using gamma-ray observations from the Interplanetary Network and find no compelling evidence for a supernova-associated burst. Based on the compact radius of the progenitor star we estimate that the shock breakout pulse was likely not detectable by current satellites.