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We report the detection of an unusual high-energy transient by the $\gamma$-ray burst detector onboard the satellite Ginga. The spectral properties of this event, which we refer to as a Medium Energy Burst (MEB900129), place it between those of Type I X-ray bursts and classical $\gamma$-ray bursts. The event was much softer than classical $\gamma$-ray bursts, with a spectrum that peaks between 16-18 keV, and decreases both above and below the peak. A thermal bremstrahlung fit to the 20-400 keV emission gives a characteristic temperature of $\approx$ 24 keV; much softer (cooler) than the $\ge 100$ keV temperatures characteristic of the classical $\gamma$-ray bursts, but similar to that of the soft $\gamma$-ray repeaters (SGRs). Although the shape of the spectrum is similar to that of type I X-ray bursts, the peak photon energy is higher by about a factor of 5. We have established with high confidence that the spectrum rolls over below 16 keV. Several spectral models which include photoelectric absorption from a neutral medium (with cosmic abundance of elements) have been fit to the data. Column densities of $\approx 10^{24} \ {\rm cm}^{-2}$ give acceptable fits to the low energy roll-over, however, a power law fit in this energy range with index $\alpha\approx -2.3$ cannot be excluded by the data. In addition, such power law models with slopes greater than $-1.5$ are strongly rejected by the data (A Rayleigh-Jeans spectrum has slope $-1.0$). The time history of the event is simple, with a rise-time of $\approx 0.7$ seconds followed by an exponential decay with a 3 second time-scale, similar to those seen from type I X-ray bursts as well as some classical $\gamma$-ray bursts, but not characteristic of the SGRs. A source radiating at $10^{38}$ erg/sec would have to be about 1 kpc distant in order to produce the measured peak flux of $\approx 1.5 \times 10^{-6}$ erg/cm$^2$/sec.
