We developed an X-ray detector using 36 arrays, each consisting of a 64-pixellated yttrium oxyorthosilicate (YSO) scintillation crystal and a 64-channel multi-anode photomultiplier tube. The X-ray detector was designed to detect X-rays with energies lower than 10 keV, primarily with the aim of localizing gamma-ray bursts (GRBs). YSO crystals have no intrinsic background, which is advantageous for increasing low-energy sensitivity. The fabricated detector was integrated into UBAT, the payload of the Ultra-Fast Flash Observatory (UFFO)/Lomonosov for GRB observation. The UFFO was successfully operated in space in a low-Earth orbit. In this paper, we present the responses of the X-ray detector of the UBAT engineering model identical to the flight model, using 241Am and 55Fe radioactive sources and an Amptek X-ray tube. We found that the X-ray detector can measure energies lower than 5 keV. As such, we expect YSO crystals to be good candidates for the X-ray detector materials for future GRB missions.