The presence of massive stars (MSs) in the region close to the Galactic Centre (GC) poses several questions about their origin. The harsh environment of the GC favours specific formation scenarios, each of which should imprint characteristic kinematic features on the MSs. We present a 2D kinematic analysis of MSs in a GC region surrounding Sgr A* based on high-precision proper motions obtained with the Hubble Space Telescope. Thanks to a careful data reduction, well-measured bright stars in our proper-motion catalogues have errors better than 0.5mas/yr. We discuss the absolute motion of the MSs in the field and their motion relative to Sgr A*, the Arches, and the Quintuplet. For the majority of the MSs, we rule out any distance further than 3-4kpc from Sgr A* using only kinematic arguments. If their membership to the GC is confirmed, most of the isolated MSs are likely not associated with either the Arches or Quintuplet clusters or Sgr A*. Only a few MSs have proper motions, suggesting that they are likely members of the Arches cluster, in agreement with previous spectroscopic results. Line-of-sight radial velocities and distances are required to shed further light on the origin of most of these massive objects. We also present an analysis of other fast-moving objects in the GC region, finding no clear excess of high-velocity escaping stars. We make our astro-photometric catalogues publicly available.