Recently, piezoelectric tactile sensors have garnered considerable attention in the field of texture recognition owing to their high sensitivity and high-frequency detection capability. Despite their remarkable potential, improving their mechanical flexibility to attach to complex surfaces remains challenging. In this study, we present a flexible piezoelectric sensor that can be bent to an extremely small radius of up to 2.5 mm and still maintain good electrical performance. The proposed sensor was fabricated by controlling the thickness that induces internal stress under external deformation. The fabricated piezoelectric sensor exhibited a high sensitivity of 9.3 nA/kPa ranging from 0 to 10 kPa and a wide frequency range of up to 1 kHz. To demonstrate real-time texture recognition by rubbing the surface of an object with our sensor, nine sets of fabric plates were prepared to reflect their material properties and surface roughness. To extract features of the objects from the detected sensing data, we converted the analog dataset to short-term Fourier transform images. Subsequently, texture recognition was performed using a convolutional neural network with a classification accuracy of 97%.