We present a detailed study of the properties of the molecular gas in the fast outflow driven by the active galactic nucleus (AGN) in the nearby radio-loud Seyfert galaxy IC 5063. By using ALMA observations of a number of tracers of the molecular gas (12CO(1-0), 12CO(2-1), 12CO(3-2), 13CO(2-1) and HCO+(4-3)), we map the differences in excitation, density and temperature of the gas as function of position and kinematics. The results show that in the immediate vicinity of the radio jet, a fast outflow, with velocities up to 800 km s-1, is occurring of which the gas has high excitation with excitation temperatures in the range 30-55 K, demonstrating the direct impact of the jet on the ISM. The relative brightness of the 12CO lines, as well as that of 13CO(2-1) vs. 12CO(2-1), show that the outflow is optically thin. We estimate the mass of the molecular outflow to be at least 1.2 × 106 M⊙ and likely to be a factor between two and three larger than this value. This is similar to that of the outflow of atomic gas, but much larger than that of the ionised outflow, showing that the outflow in IC 5063 is dominated by cold gas. The total mass outflow rate we estimated to be 12 M⊙ yr-1. The mass of the outflow is much smaller than the total gas mass of the ISM of IC 5063. Therefore, although the influence of the AGN and its radio jet is very significant in the inner regions of IC 5063, globally speaking the impact will be very modest. We used RADEX non-LTE modelling to explore the physical conditions of the molecular gas in the outflow. Models with the outflowing gas being quite clumpy give the most consistent results and our preferred solutions have kinetic temperatures in the range 20-100 K and densities between 105 and 106 cm-3. The resulting pressures are 106-107.5 K cm-3, about two orders of magnitude higher than in the outer quiescent disk. The highest densities and temperatures are found in the regions with the fastest outflow. The results strongly suggest that the outflow in IC 5063 is driven by the radio plasma jet expanding into a clumpy gaseous medium and creating a cocoon of (shocked) gas which is pushed away from the jet axis resulting in a lateral outflow, very similar to what is predicted by numerical simulations.