The study of open charm meson production provides an efficient tool for the investigation of the properties of hot and dense matter formed in nucleus–nucleus collisions. The interpretation of the existing di-muon data from the CERN SPS suffers from a lack of knowledge on the mechanism and properties of the open charm particle production. Due to this, the heavy-ion programme of the NA61/SHINE experiment at the CERN SPS has been extended by precise measurements of charm hadrons with short lifetimes. A new Vertex Detector for measurements of the rare processes of open charm production in nucleus–nucleus collisions was designed to meet the challenges of track registration and high resolution in primary and secondary vertex reconstruction. A small-acceptance version of the vertex detector was installed in 2016 and tested with Pb + Pb collisions at 150 A GeV / c. It was also operating during the physics data taking on Xe + La and Pb + Pb collisions at 150 A GeV / c conducted in 2017 and 2018. This paper presents the detector design and construction, data calibration, event reconstruction, and analysis procedure.