Texture is the embodiment of the distribution of surface microstructure. Tactile texture is a crucial factor to consider for improvement of the perception and exerting control over the environment of the material. In this study, a highly accurate and responsive tactile sensor was designed and fabricated using the inverse magnetostrictive effect of Galfenol to detect the surface microstructure of different objects and determine their roughness and fine density. Based on the Euler-Bernoulli beam dynamics theory, linear constitutive equations of magnetostrictive materials, and Faraday's law of electromagnetic induction, a relationship was established between the microstructure of the textured surface and the output voltage. The experimental results showed that the sensor had high sensitivity to object roughness recognition for roughness greater than 6.5. For fineness greater than 6, the method of extracting harmonic frequency was highly sensitive in identifying fineness. However, when the fineness was less than 6, the method of extracting the center of gravity of the power spectrum had high sensitivity for the identification of fineness. These results showed that the signal obtained by the sensor could be used to characterize the rough-smooth and sparse-fine attributes of different objects by eigenvalue extraction.