We use high-resolution (0.5 arcsec) CO(2-1) observations performed with the Atacama Large Millimetre/submillimetre Array to trace the kinematics of the molecular gas in the Seyfert 2 galaxy IC 5063. The data reveal that the kinematics of the gas is very complex. A fast outflow of molecular gas extends along the entire radio jet (~1 kpc), with the highest outflow velocities about 0.5 kpc from the nucleus, at the location of the brighter hot spot in the western lobe. The ALMA data show that a massive, fast outflow with velocities up to 650kms-1 of cold molecular gas is present, in addition to the outflow detected earlier in warm H2, H i and ionized gas. All phases of the gas outflow show similar kinematics. IC 5063 appears to be one of the be...