Evidence of AGN interaction with the IGM is observed in some galaxies and many cool core clusters. Radio jets are suspected to dig large cavities into the surrounding gas. In most cases, very large optical filaments are seen around the central galaxy. The origin of these filaments is still not understood. Star-forming regions are sometimes observed inside the filaments and are interpreted as evidence of positive feedback. Cen A is a nearby galaxy with huge optical filaments aligned with the AGN radio-jet direction. We searched for line ratio variations along the filaments, kinematic evidence of shock-broadend line widths, and large-scale dynamical structures. We observed a 1'x1' region around the inner filament of Cen A with MUSE on the VLT during Science Verification. The brightest lines detected are the Halpha, [NII], [OIII] and [SII]. MUSE shows that the filaments are made of clumpy structures inside a more diffuse medium aligned with the radio-jet axis. We find evidence of shocked shells surrounding the star-forming clumps from the line profiles, suggesting that the star formation is induced by shocks. The clump line ratios are best explained by a composite of shocks and star formation illuminated by a radiation cone from the AGN. We also report a previously undetected large arc-like structure: three streams running perpendicular to the main filament; they are kinematically, morphologically, and excitationally distinct. The clear difference in the excitation of the arcs and clumps suggests that the arcs are very likely located outside of the radiation cone and match the position of the filament only in projection. The three arcs are most consistent with neutral material swept along by a backflow of the jet plasma from the AGN outburst that is ionised through a diffuse radiation field with a low-ionisation parameter that continues to excite gas away from the radiation cone.