We report the discovery of a prominent non-thermal X-ray feature located near the Galactic centre that we identify as an energetic pulsar wind nebula. This feature, G359.95-0.04, lies 1-lyr north of Sgr A* (in projection), is comet like in shape, and has a power-law spectrum that steepens with increasing distance from the putative pulsar. The distinct spectral and spatial X-ray characteristics of the feature are similar to those belonging to the rare class of ram-pressure confined pulsar wind nebulae. The luminosity of the nebula at the distance of Sgr A*, consistent with the inferred X-ray absorptions, is Lx∼ 1 × 1034 erg s−1 in the 2–10 keV energy band. The cometary tail extends back to a region centred at the massive stellar complex IRS 13 and surrounded by an enhanced diffuse X-ray emission, which may represent an associated supernova remnant. Furthermore, the inverse Compton scattering of the strong ambient radiation by the nebula consistently explains the observed TeV emission from the Galactic centre. We also briefly discuss plausible connections of G359.95-0.04 to other high-energy sources in the region, such as the young stellar complexes IRS 13 and SNR Sgr A East.