Abstract We present a population of 19 radio-luminous supernovae (SNe) with emission reaching L _ν ∼ 10²⁶–10²⁹ erg s⁻¹ Hz⁻¹ in the first epoch of the Very Large Array Sky Survey (VLASS) at 2–4 GHz. Our sample includes one long gamma-ray burst, SN 2017iuk/GRB 171205A, and 18 core-collapse SNe detected at ≈1–60 yr after explosion. No thermonuclear explosion shows evidence for bright radio emission, and hydrogen-poor progenitors dominate the subsample of core-collapse events with spectroscopic classification at the time of explosion (79%). We interpret these findings in the context of the expected radio emission from the forward shock interaction with the circumstellar medium (CSM). We conclude that these observations require a departure from the single wind–like density profile (i.e., ρ _CSM ∝ r ⁻²) that is expected around massive stars and/or from a spherical Newtonian shock. Viable alternatives include the shock interaction with a detached, dense shell of CSM formed by a large effective progenitor mass-loss rate, M ̇ ∼ 10 − 4 – 10 − 1 M ⊙ yr⁻¹ (for an assumed wind velocity of 1000 km s⁻¹); emission from an off-axis relativistic jet entering our line of sight; or the emergence of emission from a newly born pulsar-wind nebula. The relativistic SN 2012ap that is detected 5.7 and 8.5 yr after explosion with L _ν ∼ 10²⁸ erg s⁻¹ Hz⁻¹ might constitute the first detections of an off-axis jet+cocoon system in a massive star. However, none of the VLASS SNe with archival data points are consistent with our model off-axis jet light curves. Future multiwavelength observations will distinguish among these scenarios. Our VLASS source catalogs, which were used to perform the VLASS cross-matching, are publicly available at https://doi.org/10.5281/zenodo.4895112.