Rapid processing of tactile information is essential to human haptic exploration and dexterous object manipulation. Conventional electronic skins generate frames of tactile signals upon interaction with objects. Unfortunately, they are generally ill-suited for efficient coding of temporal information and rapid feature extraction. In this work, we report a neuromorphic tactile system that uses spike timing, especially the first-spike timing, to code dynamic tactile information about touch and grasp. This strategy enables the system to seamlessly code highly dynamic information with millisecond temporal resolution on par with the biological nervous system, yielding dynamic extraction of tactile features. Upon interaction with objects, the system rapidly classifies them in the initial phase of touch and grasp, thus paving the way to fast tactile feedback desired for neuro-robotics and neuro-prosthetics.