The mechanical properties of tissues are highly correlated to the progression of various cancers. As a result, a reliable and robust method of characterizing soft material properties may be important for early cancer diagnosis in the future. Previous tactile sensors use conventional linear models to estimate the elastic properties of the tissue, thus overlooking the viscous component. We present a tactile sensor using fiber Bragg grating technology that is 15 mm in diameter for tissue palpation to characterize both the elastic and viscous properties of soft materials. We present a quasi-linear viscoelastic model that can be used in junction with the sensor to evaluate the viscoelastic properties of soft materials from ramp and hold compressions. To evaluate the proposed sensor and tissue model, we conducted palpation experiments on prostate phantoms with embedded cancerous nodules of various sizes. The results demonstrate that the sensor, equipped with the QLV model, can confidently identify the elastic and viscous properties of soft materials and can be an effective approach to distinguishing between cancerous and healthy tissue in the future.