We report on the detection of low-energy gamma-rays from the Vela supernova remnant at the similar to 9 a level with the Oriented Scintillation Spectrometer Experiment (OSSE) instrument on the Compton Gamma Ray Observatory (CGRO). The source exhibits a hard spectrum consistent with a power law of index -1.6 +/- 0.5 in the energy range 0.061 MeV to similar to 0.4 MeV. Contamination by the galactic plane and other sources was found to be insignificant. This spectrum is quite consistent with an extrapolation of the similar to(-1.7) spectrum of the 1' radius compact nebula as seen between optical and 25 keV with imaging instruments. No spectral break is seen between similar to 1 eV and 0.4 MeV, but several arguments indicate that this spectrum should cut off below 40 MeV. The extension of the nebular synchrotron emission to an energy of at least 0.4 MeV implies electron energies up to greater than or similar to 3 x 10(14) eV, which is a factor 10 below the maximum acceleration energy of 3.5 x 10(15) eV set by the polar cap vacuum potential. Imaging and spectral observations indicate that the energy in particles and magnetic field are close to equipartition in the compact nebula, with a mean field strength of similar to 6 x 10(-5) G. Even though only similar to 0.1% of the spin-down power is radiated as synchrotron photons, the inferred particle pressure in the compact nebula is about half the pulsar ram pressure L/4 pi r(2)c in the compact nebula. The relatively weak field allows electrons to escape to relatively large distances from the pulsar, which may explain why the synchrotron nebula is extended by several degrees.