NGC 2359 is an optical nebula excited by the powerful wind and the radiation of the Wolf-Rayet star HD 56925. We have investigated the interaction between this massive star and the surrounding neutral gas by analyzing the large-scale 21 cm-HI emission and by mapping the nebula in the J= 1 ->0 and the J= 2 ->1 lines of CO. We found a conspicuous (70x37pc) HI shell, expanding at 12km/s, likely produced during the main-sequence phase of the star. The molecular gas towards NGC 2359 shows three velocity components. Two of these components, A1 and A2, have narrow linewidths (1-2km/s) and radial velocities of 35-38 and 64-68km/s, respectively. The third component is detected at radial velocities between 50 and 58km/s and has a broader profile (up to 5.5km/s). Furthermore, this component is morphologicaly related with the nebula and has a velocity gradient of a few km/s. We have also estimated the physical parameters of the molecular gas by means of a LVG modelling of the CO emission. The gas projected onto the southern HII region of the nebula has low CO column density and is rather hot, probably up to 80K. Several profiles of the 13CO J= 1 ->0 line near the peak of the emission, together with a weak emission bridge between the broad and one of the narrow components (component A2), suggest the presence of a shock front acting in the southern part of the nebula. This shock was likely produced in a previous RSG/LBV phase of HD 56925.