Objectives: Adaptation of upper-limb impedance (stiffness, damping, inertia) is crucial for humans to physically interact with the external environment during grasping and manipulation tasks. Here, we present a novel framework for Adaptive Impedance Control of Upper-limb Prosthesis (AIC-UP) based on surface electromyography (sEMG) signals. Methods: AIC-UP uses muscle-tendon models driven by sEMG signals from agonist-antagonist muscle groups to estimate the human motor intent as joint kinematics, stiffness and damping. These estimates are used to implement a variable impedance controller on a simulated robot. Designed for use by amputees, joint torque or stiffness measurements are not used for model calibration. AIC-UP was evaluated with eight able-bodied subjects and a transradial amputee performing target-reaching tasks in simulation through wrist flexion-extension. The control performance was tested in free space and in the presence of unexpected perturbations. Results: We show that AIC-UP outperformed a neural network that regresses the desired kinematics from sEMG signals, in terms of robustness to muscle coactivations needed to complete the task. These results were in agreement with the qualitative feedback from the participants. Additionally, we observed that AIC-UP enables the user to adapt the stiffness and damping to the tasks at hand.