Aims: We present a new approach to study the mass-metallicity relation and its dependency on time. Methods: We used the star formation history (SFH) derived from color-magnitude diagram fitting techniques of a sample of Local Group (LG) dwarfs to obtain stellar masses, metallicities, and star-formation rates (SFR) to analyze the mass-metallicity relation as a function of the ages of their stellar populations. The accurate SFHs allow a time resolution of about 2 Gyr at the oldest ages for a total redshift range of 0 ≲ z ≲ 3. Results: The mass-metallicity relation retrieved for the sample of LG dwarfs was compared with a large dataset of literature data obtained in a wide redshift range. Neither of the two independent datasets shows a clear evolution of the mass-metallicity relation slope with redshift. However, when the star-formation rate is added as an additional parameter in the relation, it shows a dependence on the redshift in the sense that the coefficient of the mass decreases with increasing redshift, while the coefficient for the SFR is almost constant with time. This result suggests an increasing contribution with time of the galaxy stellar mass to the metalliticy of the stars that formed most recently, but it also shows that the SFR can play a fundamental role in shaping the mass-metallicity relation.