The disk mass is among the most important input parameter for every planet formation model to determine the number and masses of the planets that can form. We present an ALMA 887 μm survey of the disk population around objects from∼ 2 to 0.03 M⊙ in the nearby∼ 2 Myr old Chamaeleon I star-forming region. We detect thermal dust emission from 66 out of 93 disks, spatially resolve 34 of them, and identify two disks with large dust cavities of about 45 au in radius. Assuming isothermal and optically thin emission, we convert the 887 μm flux densities into dust disk masses, hereafter M dust. We find that the relation is steeper than linear and of the form M dust∝(M*) 1.3–1.9, where the range in the power-law index reflects two extremes of the possible relation between the average dust temperature and stellar luminosity. By reanalyzing all millimeter data available for nearby regions in a self-consistent way, we show that the 1–3 Myr old regions of Taurus, Lupus, and Chamaeleon I share the same relation, while the 10 Myr old Upper Sco association has a steeper relation. Theoretical models of grain growth, drift, and fragmentation reproduce this trend and suggest that disks are in the fragmentation-limited regime. In this regime millimeter grains will be located closer in around lower-mass stars, a prediction that can be tested with deeper and higher spatial resolution ALMA observations.