It is widely accepted that black holes with masses greater than a million solar masses (M⊙) lurk at the centres of massive galaxies. The origins of such `supermassive' black holes (SMBHs) remain unknown1, although those of stellar-mass black holes are well understood. One possible scenario is that intermediate-mass black holes (IMBHs), which are formed by the runaway coalescence of stars in young compact star clusters2, merge at the centre of a galaxy to form a SMBH3. Although many candidates for IMBHs have been proposed, none is accepted as definitive. Recently, we discovered a peculiar molecular cloud, CO-0.40-0.22, with an extremely broad velocity width, near the centre of our Milky Way galaxy. Based on the careful analysis of gas kinematics, we concluded that a compact object with a mass of about 105M⊙ is lurking in this cloud4. Here we report the detection of a point-like continuum source as well as a compact gas clump near the centre of CO-0.40-0.22. This point-like continuum source (CO-0.40-0.22*) has a wide-band spectrum consistent with 1/500 of the Galactic SMBH (Sgr A*) in luminosity. Numerical simulations around a point-like massive object reproduce the kinematics of dense molecular gas well, which suggests that CO-0.40-0.22* is one of the most promising candidates for an intermediate-mass black hole.