Sympathetic nervous system activity (SNSA) can rapidly modulate arterial stiffness, thus making it an important biomarker for SNSA evaluation. Pulse wave velocity (PWV) is a well-known quantitative indicator of arterial stiffness, but its functional responsivity to SNSA has not been elucidated. This paper reports a method to estimate rapid changes in peripheral arterial stiffness induced by SNSA using local PWV (LPWV) and to further quantify SNSA based on the estimated stiffness. LPWV was measured from the artery near the wrist to the artery near the forefinger using a biodegradable piezoelectric sensor and a photoplethysmography sensor in an electrocutaneous stimulus experiment in which pain indicts the SNSA. The relationship between LPWV, simultaneously measured peripheral arterial stiffness index, and self-reported pain intensity was quantified. The stiffness estimated by LPWV alone and the stiffness estimated by LPWV and arterial pressure both approximate the peripheral arterial stiffness index (R2 = 0.9775 and 0.9719). Pain intensity can be quantitatively evaluated in a sigmoidal relationship by either the estimated stiffness based on LPWV alone (r = 0.8594) or the estimated stiffness based on LPWV and arterial pressure (r = 0.9738). Our results demonstrated the validity of LPWV in the quantitative evaluation of SNSA and the optionality of blood pressure correction depending on application scenarios. This study advances the understanding of sympathetic innervation of peripheral arteries through the sympathetic responsivity of LPWV and contributes a quantitative biomarker for SNSA evaluation.