Touch is a crucial sense for advanced organisms, particularly humans, as it provides essential information about the shape, size, and texture of contacting objects. In robotics and automation, the integration of tactile sensors has become increasingly relevant, enabling devices to properly interact with their environment. This study aimed to develop a biomimetic, skin-inspired tactile sensor device capable of sensing applied force, characterizing it in three dimensions, and determining the point of application. The device was designed as a 4 × 4 matrix of tunneling magnetoresistive sensors, which provide a higher sensitivity in comparison to the ones based on the Hall effect, the current standard in tactile sensors. These detect magnetic field changes along a single axis, wire-bonded to a PCB and encapsulated in epoxy. This sensing array detects the magnetic field from an overlayed magnetorheological elastomer composed of Ecoflex and 5 µm neodymium–iron–boron ferromagnetic particles. Structural integrity tests showed that the device could withstand forces above 100 N, with an epoxy coverage of 0.12 mL per sensor chip. A 3D movement stage equipped with an indenting tip and force sensor was used to collect device data, which was then used to train neural network models to predict the contact location and 3D magnitude of the applied force. The magnitude-sensing model was trained on 31,260 data points, being able to accurately characterize force with a mean absolute error ranging between 0.07 and 0.17 N. The spatial sensitivity model was trained on 171,008 points and achieved a mean absolute error of 0.26 mm when predicting the location of applied force within a sensitive area of 25.5 mm × 25.5 mm using sensors spaced 4.5 mm apart. For points outside the testing range, the mean absolute error was 0.63 mm.