The Galactic Centre contains a supermassive black hole with a mass of four million Suns1 within an environment that differs markedly from that of the Galactic disk. Although the black hole is essentially quiescent in the broader context of active galactic nuclei, X-ray observations have provided evidence for energetic outbursts from its surroundings2. Also, although the levels of star formation in the Galactic Centre have been approximately constant over the past few hundred million years, there is evidence of increased short-duration bursts3, strongly influenced by the interaction of the black hole with the enhanced gas density present within the ring-like central molecular zone4 at Galactic longitude |l| < 0.7 degrees and latitude |b| < 0.2 degrees. The inner 200-parsec region is characterized by large amounts of warm molecular gas5, a high cosmic-ray ionization rate6, unusual gas chemistry, enhanced synchrotron emission7,8, and a multitude of radio-emitting magnetized filaments9, the origin of which has not been established. Here we report radio imaging that reveals a bipolar bubble structure, with an overall span of 1 degree by 3 degrees (140 parsecs × 430 parsecs), extending above and below the Galactic plane and apparently associated with the Galactic Centre. The structure is edge-brightened and bounded, with symmetry implying creation by an energetic event in the Galactic Centre. We estimate the age of the bubbles to be a few million years, with a total energy of 7 × 1052 ergs. We postulate that the progenitor event was a major contributor to the increased cosmic-ray density in the Galactic Centre, and is in turn the principal source of the relativistic particles required to power the synchrotron emission of the radio filaments within and in the vicinity of the bubble cavities.