Currently, an urgent need in the field of wearable electronics is the development of flexible sensors that can be attached to the human body to monitor various physiological indicators and movements. In this work, we propose a method for forming an electrically conductive network of multi-walled carbon nanotubes (MWCNT) in a matrix of silicone elastomer to make stretchable sensors sensitive to mechanical strain. The electrical conductivity and sensitivity characteristics of the sensor were improved by using laser exposure, through the effect of forming strong carbon nanotube (CNT) networks. The initial electrical resistance of the sensors obtained using laser technology was ~3 kOhm (in the absence of deformation) at a low concentration of nanotubes of 3 wt% in composition. For comparison, in a similar manufacturing process, but without laser exposure, the active material had significantly higher values of electrical resistance, which was ~19 kOhm in this case. The laser-fabricated sensors have a high tensile sensitivity (gauge factor ~10), linearity of >0.97, a low hysteresis of 2.4%, tensile strength of 963 kPa, and a fast strain response of 1 ms. The low Young’s modulus values of ~47 kPa and the high electrical and sensitivity characteristics of the sensors made it possible to fabricate a smart gesture recognition sensor system based on them, with a recognition accuracy of ~94%. Data reading and visualization were performed using the developed electronic unit based on the ATXMEGA8E5-AU microcontroller and software. The obtained results open great prospects for the application of flexible CNT sensors in intelligent wearable devices (IWDs) for medical and industrial applications.