Context. Classical Cepheids (CCs) are key standard candles for establishing the extragalactic distance scale through their period–luminosity (P–L) relations. While these relations are well calibrated in broadband photometric systems, their behavior in narrowband filters remains largely unexplored due to the lack of suitable observations. Combining broad- and narrowband photometry can probe wavelength-dependent extinction and provide improved constraints on the dust distribution. Aims. Our goal is to derive multiband P–L relations for CCs in the Magellanic Clouds (MCs) and construct Cepheid-based reddening maps using the Southern Photometric Local Universe Survey (S-PLUS) bands, which includes five broad bands ( u , g , r , i , z ) and seven narrow bands centered on spectral features: the Balmer jump/[OII], Ca H+K, H δ , CH g-band, Mg b triplet, H α , and the Ca triplet. Methods. We adjusted the single-epoch magnitudes of a total of more than 8000 CCs in the MCs by employing a mathematical framework to disentangle the effects of relative reddening and relative distance with respect to their host galaxies across all 12 bands. The P–L coefficients were obtained via iterative least-squares fitting and maximum likelihood optimization, with uncertainties estimated through a Bayesian Markov chain Monte Carlo (MCMC) analysis using separate fits for fundamental and overtone pulsators. Results. We present the first Cepheid P–L relations in the S-PLUS photometric system, providing independent and consistent estimates of distance and reddening. The dispersion in the P–L relations decreases systematically toward longer wavelengths, while the P-L slopes vary from about −2.0 to −2.8 in the bluest bands to about −2.9 to −3.2 in the reddest bands. The resulting reddening maps reveal spatially nonuniform extinction across both galaxies and recover known structures, such as 30 Doradus and the HI supergiant shell SGS 12 (LMC 3). The inferred geometries and orientations of the MCs are consistent with previous studies. Conclusions. Our results support that reliable distances and reddening can be recovered even from single-epoch photometry when combined with multiband data and corrected using light-curve information from other bands, enabling future high-precision 3D mapping of the MCs.