Tendon–sheath structures are commonly utilized to drive surgical robots due to their compact size, flexibility, and straightforward controllability. However, long-distance cable tension estimation poses a significant challenge due to its frictional characteristics affected by complicated factors. This paper proposes a miniature tension sensor array for an endoscopic cable-driven parallel robot, aiming to integrate sensors into the distal end of long and flexible surgical instruments to sense cable tension and alleviate friction between the tendon and sheath. The sensor array, mounted at the distal end of the robot, boasts the advantages of a small size (16 mm outer diameter) and reduced frictional impact. A force compensation strategy was presented and verified on a platform with a single cable and subsequently implemented on the robot. The robot demonstrated good performance in a series of palpation tests, exhibiting a 0.173 N average error in force estimation and a 0.213 N root-mean-square error. In blind tests, all ten participants were able to differentiate between silicone pads with varying hardness through force feedback provided by a haptic device.