We present X-ray, UV/optical, and radio observations of the stripped-envelope, core-collapse supernova (SN) 2011ei, one of the least luminous SNe IIb or Ib observed to date. Our observations begin with a discovery within similar to 1 day of explosion and span several months afterward. Early optical spectra exhibit broad, Type II-like hydrogen Balmer profiles that subside rapidly and are replaced by Type Ib-like He-rich features on a timescale of one week. High-cadence monitoring of this transition suggests absorption attributable to a high-velocity (greater than or similar to 12,000 km s(-1)) H-rich shell, which is likely present in many Type Ib events. Radio observations imply a shock velocity of v approximate to 0.13 c and a progenitor star average mass-loss rate of (M) over dot approximate to 1.4 x 10(-5) M-circle dot yr(-1) (assuming wind velocity v(w) = 10(3) km s(-1)). This is consistent with independent constraints from deep X-ray observations with Swift-XRT and Chandra. Overall, the multi-wavelength properties of SN 2011ei are consistent with the explosion of a lower-mass (3-4 M-circle dot), compact (R-* less than or similar to 1 x 10(11) cm), He-core star. The star retained a thin hydrogen envelope at the time of explosion, and was embedded in an inhomogeneous circumstellar wind suggestive of modest episodic mass loss. We conclude that SN 2011ei's rapid spectral metamorphosis is indicative of time-dependent classifications that bias estimates of the relative explosion rates for Type IIb and Ib objects, and that important information about a progenitor star's evolutionary state and mass loss immediately prior to SN explosion can be inferred from timely multi-wavelength observations.