We present a self-consistent model for the excitation of the extranuclear emission line filaments in Centaurus A. Interaction of the northern radio jet of Centaurus A with a dense cloud of material at the location of the filaments causes shock waves with velocities approximately 200-450 km s-1. The shocks produce a strong flux of EUV and soft X-ray radiation which photoionize the visible knots. We show that the mechanical flux of a mildly supersonic low-density jet is sufficient to energize the shock waves through the production of supersonic turbulent velocities in the dense cloud via the Kelvin-Helmholtz instability. Furthermore, the expected instability growth time scales, turbulent velocities, and characteristic wavelengths are all in agreement with the observations. Detailed models of cloud-cloud collisions, using the new MAPPINGS II shock and photoionization code, produce a very good fit to the observed spectra when allowance is made for shock instabilities and cloud-cloud density contrasts. The high-excitation and low-excitation forbidden lines are reproduced along with the Hbeta luminosity and temperature-sensitive [O III] lambda4363/(5007+4959) ratio. We predict the presence of a radio jet in the vicinity of the inner filaments and the presence of strong ultraviolet line fluxes in the spectrum of the filaments. The latter prediction is in contrast to the beamed photoionization models. We conclude that a narrow ionizing radiation beam is not required to produce the observed phenomena. Moreover, many properties of the knots, such as the velocity field, are deduced in the model presented here whereas they are ad hoc assumptions in a simple beamed radiation model. Similar models involving shocks with velocities greater than or similar to 200 km s-1 may also be relevant to the extended and nuclear line emission from a wide variety of active galaxies.