The reduction of fan noise in ducts is a challenging task for acoustic engineers. Usually, the confined space where an absorber can be integrated is small. In addition, one has to consider the influence of the absorber on the flow field and the attenuation of noise should be as great as possible. In this contribution, we investigate the application of a micro-perforated absorber (MPA) in the direct vicinity of a low-pressure axial fan operating at low Mach number conditions. The micro-perforated plates (MPP) are modeled using the Johnson–Champoux–Allard–Lafarge (JCAL) model for porous materials. The entire geometrical setup of duct, fan and MPA is then simulated with the Finite Element (FE) method; the pre-processing effort is reduced by using non-conforming grids to discretize the different regions. The influence of the cavity length and the positioning of the fan are analyzed. The results are then applied to the construction of a full-sized MPA duct component that takes the limited space into consideration. Simulation results and overall functionality are compared to experimental results obtained in an axial-fan test rig. The Finite Element framework proved to be robust in predicting overall sound pressure level reduction in the higher volume flow rates. It is also shown that the MPP increases sound reduction in the low-frequency regime and at two resonant frequencies of the MPA setup. However, its main benefit lies in maintaining the efficiency of the fan. The location of the fan downstream or within the MPA has a significant effect on both the simulated and measured sound reduction.