Context. A total of four long-duration gamma-ray bursts (GRBs) have been confirmed at very high-energy (≥100GeV) with high significance, and any possible peculiarities of these bursts will become clearer as the number of detected events increases. Multi-wavelength follow-up campaigns are required to extract information on the physical conditions within the jets that lead to the very high-energy counterpart, hence they are crucial to reveal the properties of this class of bursts. Aims. GRB 201015A is a long-duration GRB detected using the MAGIC telescopes from ~40 s after the burst. If confirmed, this would be the fifth and least luminous GRB ever detected at these energies. The goal of this work is to constrain the global and microphysical parameters of its afterglow phase, and to discuss the main properties of this burst in a broader context. Methods. Since the radio band, together with frequent optical and X-ray observations, proved to be a fundamental tool for overcoming the degeneracy in the afterglow modelling, we performed a radio follow-up of GRB 201015A over 12 different epochs, from 1.4 days (2020 October 17) to 117 days (2021 February 9) post-burst, with the Karl G. Jansky Very Large Array, e-MERLIN, and the European VLBI Network. We include optical and X-ray observations, performed respectively with the Multiple Mirror Telescope and the Chandra X-ray Observatory, together with publicly available data, in order to build multi-wavelength light curves and to compare them with the standard fireball model. Results. We detected a point-like transient, consistent with the position of GRB 201015A until 23 and 47 days post-burst at 1.5 and 5 GHz, respectively. No emission was detected in subsequent radio observations. The source was also detected in optical (1.4 and 2.2 days post-burst) and in X-ray (8.4 and 13.6 days post-burst) observations. Conclusions. The multi-wavelength afterglow light curves can be explained with the standard model for a GRB seen on-axis, which expands and decelerates into a medium with a homogeneous density. A circumburst medium with a wind-like profile is disfavoured. Notwithstanding the high resolution provided by the VLBI, we could not pinpoint any expansion or centroid displacement of the outflow. If the GRB is seen at the viewing angle θ that maximises the apparent velocity β_app (i.e. θ ~ β_app^-1), we estimate that the Lorentz factor for the possible proper motion is Г_α ≤ 40 in right ascension and Г_δ ≤ 61 in declination. On the other hand, if the GRB is seen on-axis, the size of the afterglow is ≤5pc and ≤16pc at 25 and 47 days. Finally, the early peak in the optical light curve suggests the presence of a reverse shock component before 0.01 days from the burst.