We present a measurement of the evolution of the stellar mass function in four redshift bins at 0.4 < z < 1.2, using a sample of more than 5000 K-selected galaxies drawn from the MUNICS (Munich Near-Infrared Cluster Survey) data set. Our data cover the stellar mass range 10¹⁰ h^-2 M ≤ M ≤ 10¹² h^-2 M. We derive K-band mass-to-light ratios by fitting a grid of composite stellar population models of varying star formation history, age, and dust extinction to BVRIJK photometry. We discuss the evolution of the average mass-to-light ratio as a function of galaxy stellar mass in the K and B bands. We compare our stellar mass function at z > 0 to estimates obtained similarly at z = 0. We find that the mass-to-light ratios in the K band decline with redshift. This decline is similar for all stellar masses above 10¹⁰ h^-2 M. Lower mass galaxies have lower mass-to-light ratios at all redshifts. The stellar mass function evolves significantly to z = 1.2. The total normalization decreases by a factor of ~2, the characteristic mass (the knee) shifts toward lower masses, and the bright end therefore steepens with redshift. The amount of number density evolution is a strong function of stellar mass, with more massive systems showing faster evolution than less massive systems. We discuss the total stellar mass density of the universe and compare our results to the values from the literature at both lower and higher redshifts. We find that the stellar mass density at z ~ 1 is roughly 50% of the local value. Our results imply that the mass assembly of galaxies continues well after z ~ 1. Our data favor a scenario in which the growth of the most massive galaxies is dominated by accretion and merging rather than star formation, which plays a larger role in the growth of less massive systems.