Stellar magnetic activity is a source of noise in the study of the transits of extrasolar planets. It induces flux variations that significantly affect the transit depth determination and the derivations of planetary and stellar parameters. Furthermore, the colour dependence of stellar activity may significantly influence the characterization of planetary atmospheres. Here we present a systematic approach to quantify the corresponding stellar flux variations as a function of wavelength bands. We consider a star with spots covering a given fraction of its disc and model the variability in both the UBVRIJHK photometric system and the Spitzer/IRAC wavebands for dwarf stars from G to M spectral types. We compare activity-induced flux variations in different passbands with planetary transits and quantify how they affect the determination of the planetary radius and the analysis of the transmission spectroscopy in the study of planetary atmospheres. We suggest that the monitoring of the systems by using broad-band photometry, from visible to infrared, helps us to constrain activity effects. The ratio of the relative variations in the stellar fluxes at short wavelength optical bands (e.g., U or B) to near-infrared ones (e.g., J or K) can be used to distinguish starspot brightness dips from planetary transits in a stellar light curve. In addition to the perturbations in the measurement of the planetary radius, we find that starspots can affect the determinations of both the relative semimajor axis and the inclination of the planetary orbit, which have a significant impact on the derivation of the stellar density from the transit light curves.