In this paper a new paradigm for prediction of wind turbine wakes is proposed, which is based on a reduced order model (ROM) embedded in a Kalman filter. The ROM is evaluated by means of dynamic mode decomposition performed on high fidelity LES numerical simulations of wind turbines operating under different operational regimes. The ROM enables to capture the main physical processes underpinning the downstream evolution and dynamics of wind turbine wakes. The ROM is then embedded within a Kalman filter in order to produce a time-marching algorithm for prediction of wind turbine wake flows. This data-driven algorithm enables data assimilation of new measurements simultaneously to the wake prediction, which leads to an improved accuracy and a dynamic update of the ROM in presence of emerging coherent wake dynamics observed from new available data. Thanks to its low computational cost, this numerical tool is particularly suitable for real-time applications, control and optimization of large wind farms.