Intermediate-mass black holes (IMBHs) are among the most elusive objects in contemporary astrophysics. Both theoretical and observational evidence of their existence are subject of debate. Conversely, both theory and observations confirm the presence of a large population of millisecond pulsars (MSPs) with low-mass companions residing in globular cluster (GC) centres. If IMBHs are common in GC centres as well, then dynamical interactions will inevitably break up many of these binaries, causing the ejection of several fast MSPs in the Galactic halo. Such population of fast halo MSPs, hard to produce with ‘standard’ MSP generation mechanisms, would provide a strong, albeit indirect, evidence of the presence of a substantial population of IMBHs in GCs. In this paper, we study in detail the dynamical formation and evolution of such fast MSPs population, highlighting the relevant observational properties and assessing detection prospects with forthcoming radio surveys.