The ASTRI Mini-Array is an international project to build and operate an array of nine small-sized (4-m diameter) Imaging Atmospheric Cherenkov Telescopes (IACTs) at the Observatorio del Teide (Tenerife, Spain). The array is designed to perform deep galactic and extragalactic gamma-ray sky observations in the 1–200 TeV energy band. As part of the overall software system, the ASTRI team is developing a dedicated Data Processing System consisting of specific software components that implement all the functionalities needed to achieve the final science products from raw data. The main software components are the Cherenkov Camera Pre-Processing (for offline conversion from binary to FITS data format of Cherenkov camera raw data), the Stereo Event Builder (for offline stereo array trigger of Cherenkov events), the Cherenkov Data Pipeline (for data reduction and analysis), and the Calibration Software (for all required calibrations). An additional components for Stellar Intensity Interferometry data analysis is also envisaged. Thanks to the high-speed network connection available between Tenerife and Italy and the low data volume produced by the innovative ASTRI cameras, raw data files acquired onsite will be delivered to the ASTRI Data Center in Rome immediately after acquisition. At the Data Center, the Data Processing System will automatically perform the pre-processing, software stereo trigger, calibration, reduction, and analysis of the raw data up to the generation of science-ready data (event-lists and Instrument Response Function, to be delivered to the science community) as well as of automated science products. In this contribution we present the main features and components of the ASTRI Data Processing System and report on the status of its development and implementation.