In the present paper, a new microwave-radar-based technique for short-range detection and classification of multiple human and vehicle targets crossing a monitored area is proposed. This approach, which can find applications in both security and infrastructure surveillance, relies upon the processing of the scattered-field data acquired by low-cost off-the-shelf components, i.e., a 24 GHz Frequency Modulated Continuous Wave radar module and a Raspberry Pi mini-PC. The developed method is based on an ad-hoc processing chain to accomplish the automatic target recognition task, which consists of blocks performing clutter and leakage removal with an IIR filter, clustering with a DBSCAN approach, tracking using a Benedict-Bordner α-β filter, features extraction, and finally classification of targets by means of a -Nearest Neighbor algorithm. The approach is validated in real experimental scenarios, showing its capabilities in correctly detecting multiple targets belonging to different classes (i.e., pedestrians, cars, motorcycles, and trucks).