  Classical novae are the most common astrophysical thermonuclear explosions,
occurring on the surfaces of white dwarf stars accreting gas from companions in
binary star systems. Novae typically expel ~10^(-4) solar masses of material at
velocities exceeding 1,000 kilometres per second. However, the mechanism of
mass ejection in novae is poorly understood, and could be dominated by the
impulsive flash of thermonuclear energy, prolonged optically thick winds, or
binary interaction with the nova envelope. Classical novae are now routinely
detected in gigaelectronvolt gamma-ray wavelengths, suggesting that
relativistic particles are accelerated by strong shocks in the ejecta. Here we
report high-resolution radio imaging of the gamma-ray-emitting nova V959 Mon.
We find that its ejecta were shaped by the motion of the binary system: some
gas was expelled rapidly along the poles as a wind from the white dwarf, while
denser material drifted out along the equatorial plane, propelled by orbital
motion. At the interface between the equatorial and polar regions, we observe
synchrotron emission indicative of shocks and relativistic particle
acceleration, thereby pinpointing the location of gamma-ray production. Binary
shaping of the nova ejecta and associated internal shocks are expected to be
widespread among novae, explaining why many novae are gamma-ray emitters.
