ASTRI (Astrofisica con Specchi a Tecnologia Replicante Italiana) is a Flagship Project financed by the Italian Ministry of Education, University and Research, and led by INAF, the Italian National Institute of Astrophysics. The main goals of the ASTRI project are the realization of an end-to-end prototype of a Small Size Telescope (SST) for the Cherenkov Telescope Array (CTA) in a dual- mirror configuration (SST-2M) and, subsequently, of a mini-array comprising seven SST-2M telescopes. The mini-array will be placed at the final CTA Southern Site, which will be part of the CTA seed array, around which the whole CTA observatory will be developed. The Mini-Array Software System (MASS) will provide a comprehensive set of tools to prepare an observing proposal, to perform the observations specified therein (monitoring and controlling all the hardware components of each telescope), to analyze the acquired data online and to store/retrieve all the data products to/from the archive. Here we present the main features of the MASS and its first version, to be tested on the ASTRI SST-2M prototype that will be installed at the INAF observing station located at Serra La Nave on Mount Etna in Sicily.