This contribution is concerned with water absorption in poly(butylene adipate terephthalate) filled with two different fillers, taken from the mesocarp and epicarp of the fruit of babassu palm tree. Neat PBAT and 10% and 20% PBAT/babassu compounds were tested at ambient temperature for 90 days, in order to estimate the water absorption capacity and kinetics. The incorporation of filler increases the absorption capacity 3.5 to 15 times over the values measured for the neat matrix, depending on filler type and content, showing a strong nonlinearity at higher absorption levels. Initial absorption kinetics follows Fick’s law for pure PBAT. Anomalous (non Fickean) diffusion was observed in the compounds, with kinetic parameters independent of the loading level, but dependent on filler type.