We report quantitative photoacoustic elastography (QPAE) capable of measuring Young’s modulus of biological tissue in vivo in humans. By combining conventional PAE with a stress sensor having known stress–strain behavior, QPAE can simultaneously measure strain and stress, from which Young’s modulus is calculated. We first demonstrate the feasibility of QPAE in agar phantoms with different concentrations. The measured Young’s modulus values fit well with both the empirical expectation based on the agar concentrations and those measured in an independent standard compression test. Next, QPAE was applied to quantify the Young’s modulus of skeletal muscle in vivo in humans, showing a linear relationship between muscle stiffness and loading. The results demonstrated the capability of QPAE to assess the absolute elasticity of biological tissue noninvasively in vivo in humans, indicating its potential for tissue biomechanics studies and clinical applications.