This work shows the development and characterization of a fiber optic tactile sensor based on Fiber Bragg Grating (FBG) technology. The sensor is a 3×3 array of FBGs encapsulated in a PDMS compliant polymer. The strain experienced by each FBG is transduced into a Bragg wavelength shift and the inverse characteristics of the sensor were computed by means of a feedforward neural network. A 21 mN RMSE error was achieved in estimating the force over the 8 N experimented load range while including all probing sites in the neural network training procedure, whereas the median force RMSE was 199 mN across the 200 instances of a Monte Carlo randomized selection of experimental sessions to evaluate the calibration under generalized probing conditions. The static metrological properties and the possibility to fabricate sensors with relatively high spatial resolution make the proposed design attractive for the sensorization of robotic hands. Furthermore, the proved MRI-compatibility of the sensor opens other application scenarios, such as the possibility to employ the array for force measurement during functional MRI-measured brain activation.