Intermediate-mass black holes should help us to understand the evolutionary connection between stellar-mass and super-massive black holes(1). However, the existence of intermediate-mass black holes is still uncertain, and their formation process is therefore unknown(2). It has long been suspected that black holes with masses 100 to 10,000 times that of the Sun should form and reside in dense stellar systems(3-6). Therefore, dedicated observational campaigns have targeted globular clusters for many decades, searching for signatures of these elusive objects. All candidate signatures appear radio-dim and do not have the X-ray to radio flux ratios required for accreting black holes(7). Based on the lack of an electromagnetic counterpart, upper limits of 2,060 and 470 solar masses have been placed on the mass of a putative black hole in 47 Tucanae (NGC 104) from radio and X-ray observations, respectively(8,9). Here we show there is evidence for a central black hole in 47 Tucanae with a mass of 2, 200(-800)(+1,500) solar masses when the dynamical state of the globular cluster is probed with pulsars. The existence of an intermediate-mass black hole in the centre of one of the densest clusters with no detectable electromagnetic counterpart suggests that the black hole is not accreting at a sufficient rate to make it electromagnetically bright and therefore, contrary to expectations, is gas-starved. This intermediate-mass black hole might be a member of an electromagnetically invisible population of black holes that grow into supermassive black holes in galaxies.