We have analysed the photometric data obtained with the STEREO spacecraft for 558 non-magnetic chemically peculiar (CP) stars to search for rotational and pulsational variability. Applying the Lomb–Scargle and the phase dispersion minimization methods, we have detected photometric variability for 44 objects from which 35 were previously unknown. The new objects are all bright stars on the ecliptic plane (magnitude range 4.7 < V < 11.7) and will therefore be of great interest to studies of stellar structure and evolution. In particular, several show multiple signals consistent with hybrid δ Scuti and γ Doradus pulsation, with different periodicities allowing very different regions of the stellar interior to be studied. There are two subgroups of stars in our sample: the cool metallic line Am (CP1) and the hot HgMn (CP3) stars. These objects fall well inside the classical instability strip where δ Scuti, γ Doradus and slowly pulsating B-type stars are located. We also expect to find periods correlated to the orbital period for CP1 objects as they are mostly members of binary systems. For CP3 stars, rotationally induced variability is still a matter of debate. Although surface spots were detected, they are believed to produce only marginal photometric amplitudes. So, periods from several hours to a few days were expected for these two star groups. The STEREO/HI-1 data are well matched to studies of this frequency domain, owing to the cadence of approximately 40 min and multiple epochs over four and a half years. The remaining 514 stars are likely to be constant in the investigated range from 0.1 to 10 d. 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. We discuss our results in comparison to already published ones and find a very good agreement. Finally, we have calibrated the variable stars in terms of the effective temperature and luminosity in order to estimate masses and ages. For this purpose, we used specifically developed calibrations for CP stars and, when available, Hipparcos parallaxes. All but two objects cover the stellar mass range from 1.5 to 5 M⊙ and are located between the zero- and terminal-age main sequence.