Context. The stellar mass (M_⋆) and the star formation rate (SFR) are among the most important features that characterize galaxies. Measuring these fundamental properties accurately is critical for understanding the present state of galaxies, their history, and future evolution. Infrared (IR) photometry is widely used to measure the M_⋆ and SFR of galaxies because the near-IR traces the continuum emission of the majority of their stellar populations (SPs), and the mid/far-IR traces the dust emission powered by star-forming activity. Aims. This work explores the dependence of the IR emission of galaxies on their extinction, and the age of their SPs. It aims to provide accurate and precise IR-photometry SFR and M_⋆ calibrations that account for SP age and extinction while providing quantification of their scatter. Methods. We used the CIGALE spectral energy distribution (SED) fitting code to create model SEDs of galaxies with a wide range of star formation histories, dust content, and interstellar medium properties. We fit the relations between M_⋆ and SFR with IR and optical photometry of the model-galaxy SEDs with the Markov chain Monte Carlo (MCMC) method. As an independent confirmation of the MCMC fitting method, we performed a machine-learning random forest (RF) analysis on the same data set. The RF model yields similar results to the MCMC fits, thus validating the latter. Results. This work provides calibrations for the SFR using a combination of the WISE bands 1 and 3, or the JWST NIR-F200W and MIRI-F2100W. It also provides mass-to-light ratio calibrations based on the WISE band-1, the JWST NIR-F200W, and the optical u − r or g − r colors. These calibrations account for the biases attributed to the SP age, while they are given in the form of extinction-dependent and extinction-independent relations. Conclusions. The proposed calibrations show robust estimations while minimizing the scatter and biases throughout a wide range of SFRs and stellar masses. The SFR calibration offers better results, especially in dust-free or passive galaxies where the contributions of old SPs or biases from the lack of dust are significant. Similarly, the M_⋆ calibration yields significantly better results for dusty and high-SFR galaxies where dust emission can otherwise bias the estimations.