Fiber-shaped sensors have great potential for real-time monitoring of human physiological signals thanks to the merging of electronic and textile technologies. This work reports on the fabrication of a core–sheath structured strain-sensing fiber based on the wet-spinning method. The sensing fiber is composed of a core of non-conducting polyurethane and a conducting sheath of carbon black in a polyurethane matrix. Microscopic observation reveals the irregular shape or scattered appearance of the core as well as the porous structure of the fiber, the diameter of which is in the range 200–500 μm. The electro-mechanical properties and their dependence on carbon black concentration in the sheath and draw ratio between the spinneret and first drafting roller are experimentally investigated. It has been found that the percolation threshold of the fiber is in the range 15–16 wt%. The resistance of the fiber rises stably as the fiber is stretched up to a strain of 120% and increases with the increase of draw ratio between the spinneret and first drafting roller. In the cyclic tensile tests, the resistance of the fiber exhibits good repeatability in subsequent loading–unloading cycles after pre-stretching, despite partial recovery of the resistance in the first few cycles. The integration of the strain-sensing fiber into textiles is demonstrated by the core-spun yarn fabricated based on a modified vortex spinning method. The results of this study indicate the fiber could be a promising candidate for a sensor for smart textiles.