We use Gaia-TGAS data to compare the transverse velocities in Galactic longitude (coming from proper motions and parallaxes) in the Milky Way disk for negative and positive longitudes as a function of distance. The transverse velocities are strongly asymmetric and deviate significantly from the expectations for an axisymmetric galaxy. The value and sign of the asymmetry changes at spatial scales of several tens of degrees in Galactic longitude and about 0.5 kpc in distance. The asymmetry is statistically significant at 95% confidence level for 57% of the region probed, which extends up to 1.2 kpc. A percentage of 24% of the region shows absolute differences at this confidence level larger than 5 km s-1 and 7% larger than 10 km s-1. The asymmetry pattern shows mild variations in the vertical direction and with stellar type. A first qualitative comparison with spiral arm models indicates that the arms are probably not the main source of the asymmetry. We briefly discuss alternative origins. This is the first time that global all-sky asymmetries are detected in the Milky Way kinematics beyond the local neighbourhood and with a purely astrometric sample.