The ASTRI Mini-Array is a project for the Cherenkov astronomy in the TeV energy range. ASTRI Mini-Array consists of nine Imaging Atmospheric Cherenkov telescopes located at the Teide Observatory (Canarias Islands). Large volumes of monitoring and logging data result from the operation of a large-scale astrophysical observatory. In the last few years, several "Big Data" technologies have been developed to deal with such volumes of data, especially in the Internet of Things (IoT) framework. We present the Monitoring, Logging, and Alarm (MLA) system for the ASTRI Mini-Array aimed at supporting the analysis of scientific data and improving the operational activities of the telescope facility. The MLA system was designed and built considering the latest software tools and concepts coming from Big Data and IoT to respond to the challenges posed by the operation of the array. A particular relevance has been given to satisfying the reliability, availability, and maintainability requirements towards all the array sub-systems and auxiliary devices. The system architecture has been designed to scale up with the number of devices to be monitored and with the number of software components to be considered in the distributed logging system.