Context. Young stellar objects (YSOs) are surrounded by protoplanetary disks, which are the birthplace of young planets. Ring and gap structures are observed among evolved protoplanetary disks, often interpreted as a consequence of planet formation. Aims. The pre-Main Sequence (pre-MS) star MP Mus hosts one of the few known examples of protoplanetary disks within 100 pc. Previously, a disk ring structure, with a radius of 80-85 au, was detected in scattered light via near-infrared polarimetric imaging. This ring structure may be indicative of the disk clearing process. Although such ring structures were not seen in the ALMA Band 6 images, some features were detected at ∼50 au. Methods. In this paper, we analyzed new ALMA Band 7 observations of MP Mus in order to investigate the details of its disk substructures. Results. By subtracting the continuum profile generated from Band 7 data, we discovered a ring structure in the Band 7 dust continuum image at ∼50 au. We calculated the overall dust mass as 28.4 ± 2.8 M⊙ at 0.89 mm and 26.3 ± 2.6 M⊙ at 1.3 mm and the millimeter spectral index α0.89-1.3 mm ∼2.2 ± 0.3 between 0.89 mm and 1.3 mm. Moreover, we display the spatial distribution of the spectral index (αmm), estimating values ranging from 1.3 at the inner disk to 4.0 at a large radius. Additionally, we observed an extended gas disk up to ∼120 au, in contrast with a compact continuum millimeter extent of ∼60 au. Conclusions. We conclude that there are strong indicators for an active radial drift process within the disk. However, we cannot discard the possibility of a dust evolution process and a grain growth process as responsible for the outer disk structures observed in the ALMA continuum imaging.