The Sentinel-2 MultiSpectral Instrument (MSI) collects multiple spectral band images, corresponding to specific sensing wavelengths and spatial resolutions, i.e. 10 m, 20 m and 60 m, respectively. Images are collected one at the time with a given time-lag between observations. Under favorable conditions, spatio-temporal characteristics of propagating ocean surface waves can thus uniquely be retrieved. A method for surface current vector field reconstruction is then developed. Demonstrated over different deep ocean regions, the retrieved surface current fields well compare with medium-resolution ocean circulation model or derived-velocities from altimeter measurements. At finer scales, the surface wave-conservation law is recovered, with the associated relationship between current vorticity and wave-ray curvature. Over shallow water regions, the wave propagation properties well follow sea depth variations, consistent with ETOPO1 data. Finally, time-lag between detector bands can also be exploited to estimate speed and direction properties of detected surface wave breaking whitecaps. An analysis of velocity reconstruction errors further reveals that Sentinel-2 MSI inter-channel co-registration is realized with an accuracy better than 0.1 pixel. Overall, these results confirm very promising capabilities of optical imagery to provide direct surface current velocity measurements from space, over relatively large areas, O(100 km), with a spatial resolution down to O(1 km).