The Auger Muons and Infill for the Ground Array (AMIGA) is an enhancement of the Pierre Auger Observatory, whose purpose is to lower the energy threshold of the observatory down to $10^{16.5}$ eV, and to measure the muonic content of air showers directly. These measurements will significantly contribute to the determination of primary particle masses in the range between the second knee and the ankle, to the study of hadronic interaction models with air showers, and, in turn, to the understanding of the muon puzzle. The underground muon detector of AMIGA is concomitant to two triangular grids of water-Cherenkov stations with spacings of 433 and 750 m; each grid position is equipped with a 30\,m$^2$ plastic scintillator buried at 2.3 m depth. After the engineering array completion in early 2018 and general improvements to the design, the production phase commenced. In this work, we report on the status of the underground muon detector, the progress of its deployment, and the performance achieved after two years of operation. The detector construction is foreseen to finish by mid-2022.