The XRISM/Resolve microcalorimeter directly measured the gas velocities in the core of the Virgo Cluster, the closest example of AGN feedback in a cluster. This proximity allows us to resolve the kinematic impact of feedback on scales down to 5 kpc. Our spectral analysis reveals a high velocity dispersion of $σ_v$=262 (+45 / -38) km/s near the AGN, which steeply declines to ~60 km/s between 5 and 25 kpc in the northwest direction. The observed line-of-sight bulk velocity in all regions is broadly consistent with the central galaxy, M87, with a mild trend toward blueshifted motions at larger radii. Systematic uncertainties have been carefully assessed and do not affect the measurements. The central velocities, if attributed entirely to isotropic turbulence, correspond to a transonic ICM at sub-6 kpc scales with three-dimensional Mach number 0.69 (+0.14 / -0.11) and a non-thermal pressure fraction of 21 (+7 / -5)%. Simple models of weak shocks and sound waves and calculations assuming isotropic turbulence both support the hypothesis that the velocity field reflects a mix of shock-driven expansion and turbulence. Compared to other clusters observed by XRISM to date, M87's central region stands out as the most kinematically disturbed, exhibiting both the highest velocity dispersion and the largest 3D Mach number, concentrated at the smallest physical scales.