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We compute precise values of quasinormal modes of a massive scalar field in the background of the Schwarzschild-like brane-localised black holes. It is shown that the quasinormal spectrum of the massive field differs qualitatively from that previously known for other black hole models, due to the presence of two kinds of modes: those whose damping rate vanishes as the mass of the field mu increases up to some critical value, and those whose real oscillation frequency vanishes at a certain value of mu. While the first type of modes, which are arbitrarily long-lived, are recognized in various four-dimensional backgrounds as quasi-resonances, the second type is a novel feature for asymptotically flat black holes. When Re(omega) reaches zero, the fundamental mode disappears from the spectrum and the first overtone becomes the fundamental mode. We also demonstrate that quasi-resonances may not exist for brane-localised black holes immersed in D >= 6 - dimensional bulk.