Context. In the spectra of variable pulsating stars, especially Mira stars, the detection of intense hydrogen emission lines has been explained by the presence of a radiative and hypersonic shock wave, periodically propagating throughout the stellar atmosphere. Previous observation of the Mira star o Ceti around one of its brightest maximum light led to the detection of a strong level of linear polarization associated to Balmer emissions, although the origin of this phenomenon is not fully explained yet. Aims: With the help of spectropolarimetry, we propose to investigate the nature of shock waves propagating throughout the stellar atmosphere and present, for o Ceti (the prototype of Mira stars), a full observational study of hydrogen emission lines formed in the radiative region of such a shock. Methods: Using the instrument NARVAL mounted on the Télescope Bernard Lyot (TBL) in Pic du Midi Observatory (France), we performed a spectropolarimetric monitoring of o Ceti during three consecutive pulsation cycles. For this survey, the four Stokes parameters (I for intensity, Q and U for linear polarization, and V for circular polarization) were systematically collected, with a particular emphasis on the maxima of luminosity, i.e. when a radiative shock wave is supposed to emerge from the photosphere and starts to propagate outward. Results: On hydrogen Balmer lines, over a large part of the luminosity cycle, we report clear detection of polarimetric structures in Q and U Stokes spectra (and also in V Stokes spectra but to a lesser extent). We report a temporal evolution of these spectropolarimetric signatures, which appear strongly correlated to the presence of an intense shock wave responsible for the hydrogen emission lines. We establish that the hydrogen lines are polarized by a physical process inherent to the mechanism responsible for the emission line formation: the shock wave itself. Two mechanisms are thus considered: a global one that implies a polarization induced by some giant convective cells located around the photosphere and a local one that implies a charge separation due to the passage of the shock wave, inducing an electrical current. Combined with the existing turbulence, this may generate a magnetic field, hence polarization. Based on spectropolarimetric observations obtained at the Télescope Bernard Lyot (TBL at Observatoire du Pic du Midi, CNRS and Université de Toulouse, France).