Context. So far, surface magnetic fields have never been detected on Mira stars. Only recently have the spectropolarimetric capabilities of measuring it via the Zeeman effect become available to us. Then, to complete the knowledge of the magnetic field and of its influence during the transition from asymptotic giant branch to planetary nebulae stages, we have undertaken a search for magnetic fields on the surface of Mira stars. Aims: Our main goal is to constrain - at this stage of stellar evolution - the surface magnetic field (presence and strength) and to define the magnetic field strength dependence along the radial distance to the star, above the photosphere and across the circumstellar envelope of cool and evolved stars. Methods: We used spectropolarimetric observations (Stokes V spectra probing circular polarization), collected with the Narval instrument at TBL, in order to detect - with the least squares deconvolution (LSD) method - a Zeeman signature in the visible part of the spectrum. Results: We present the first spectropolarimetric observations of the S-type Mira star χ Cyg, performed around its maximum light. We detected a polarimetric signal in the Stokes V spectra and established its Zeeman origin. We claim that it is likely to be related to a weak magnetic field present at the photospheric level and in the lower part of the stellar atmosphere. We estimated the strength of its longitudinal component to about 2-3 gauss. This result favors a 1/r law for the variation in the magnetic field strength across the circumstellar envelope of χ Cyg. This is the first detection of a weak magnetic field on the stellar surface of a Mira star, and we discuss its origin in the framework of shock waves periodically propagating throughout the atmosphere of these radially pulsating stars. Conclusions: At the date of our observations of χ Cyg, the shock wave reaches its maximum intensity, and it is likely that the shock amplifies a weak stellar magnetic field during its passage through the atmosphere. Without such an amplification by the shock, the magnetic field strength would have been too low to be detected. For the first time, we also report strong Stokes Q and U signatures (linear polarization) centered on the zero velocity (i.e., on the shock front position). They seem to indicate that the radial direction would be favored by the shock during its propagation throughout the atmosphere. Based on observations obtained at the Télescope Bernard Lyot (TBL, USR5026) at the Observatoire du Pic du Midi, operated by the Observatoire Midi-Pyrénées, Université de Toulouse (Paul Sabatier), Centre National de la Recherche Scientifique of France.