Context. Sun-like stars are promising candidates to host exoplanets and are often included in exoplanet surveys by radial velocity (RV) and direct imaging. In this paper we report on the detection of a stellar companion to the nearby solar-analogue star HD 104304, which previously was considered to host a planetary mass or brown dwarf companion. Aims: We searched for close stellar and substellar companions around extrasolar planet host stars with high angular resolution imaging to characterize planet formation environments. Methods: The detection of the stellar companion was achieved by high angular resolution measurements, using the ``Lucky Imaging'' technique at the ESO NTT 3.5 m with the AstraLux Sur instrument. We combined the results with VLT/NACO archive data, where the companion could also be detected. The results were compared to precise RV measurements of HD 104304, obtained at the Lick and Keck observatories from 2001-2010. Results: We confirmed common proper motion of the binary system. A spectral type of M4V of the companion and a mass of 0.21 M_&sun; was derived. Due to comparison of the data with RV measurements of the unconfirmed planet candidate listed in the Extrasolar Planets Encyclopaedia, we suggest that the discovered companion is the origin of the RV trend and that the inclination of the orbit of i≈35°explains the relatively small RV signal. Based on observations made with ESO Telescopes at the La Silla and Paranal Observatory under programme IDs 083.C-0145 and 084.C-0812, and on data obtained from the ESO Science Archive Facility.