Mechanical-biological treatment of municipal solid waste (MSW) facilitates reducing the landfill workload. The current research aimed to study general activity parameters, content, functions, and diversity of fungal and prokaryotic microbiota in mechanically separated organic fraction of MSW (ms-OFMSW) composting, without using bulking agents and process-promoting additives. During 35 days of composting, vigorous emission of CO2 (max. 129.4 mg CO2 kg−1 h−1), NH3 (max. 0.245 mg NH3 kg−1 h−1), and heat release (max. 4.28 kJ kg−1 h−1) occurred, indicating intense microbial activity. Immediately following the preparation of the composting mixture, eight genera of lactic acid bacteria and fungal genera Rhizopus, Aspergillus, Penicillium, Agaricus, and Candida were predominant. When the temperature increased to more than 60 °C, the microbial biodiversity decreased. Due to succession, the main decomposers of ms-OFMSW changed. The Bacillaceae family, the genera Planifilum, Thermobifida, and Streptomyces, and the fungal genera Thermomyces and Microascus were involved in the processes of organic matter mineralization at the high-temperature and later stages. The biodiversity of the microbiota increased at the stages of cooling and maturation under conditions of relatively high nitrogen content. Thus, the microbial community and its succession during ms-OFMSW composting were characterized for the first time in this work.