About 10 per cent of upper main-sequence stars are characterized by the presence of chemical peculiarities, often found together with a structured magnetic field. The atmospheres of most of those chemically peculiar stars present surface spots, leading to photometric variability caused by rotational modulation. The study of the light curves of those stars therefore permits a precise measurement of their rotational period, which is important to study stellar evolution and to plan further detailed observations. We analysed the light curves of 1028 chemically peculiar stars obtained with the STEREO spacecraft. We present here the results obtained for the 337 magnetic chemically peculiar stars in our sample. Thanks to the cadence and stability of the photometry, STEREO data are perfectly suitable to study variability signals with a periodicity typical of magnetic chemically peculiar stars. Using a matched filter algorithm and then two different period searching algorithms, we compiled a list of 82 magnetic chemically peculiar stars for which we measured a reliable rotational period; for 48 of them, this is the first measurement of their rotational period. The remaining 255 stars are likely to be constant, although we cannot exclude the presence of long-period variability. In some cases, the presence of blending or systematic effects prevented us from detecting any reliable variability and in those cases we classified the star as constant. For each star we classified as variable, we determined temperature, luminosity, mass and fractional age, but the limited statistics, biased towards the shorter periods, prevented us from finding any evolutionary trend of the rotational period. For a few stars, the comparison between their projected rotational velocity and equatorial velocity let us believe that their real rotational period might be longer than that found here and previously obtained. For the 82 stars identified as variable, we give all necessary information needed to plan further phase-dependent observations.