In this paper, the problem of a fully actuated hexarotor performing a physical interaction with the environment through a rigidly attached tool is considered. A nonlinear model predictive impedance control (NMPIC) method is proposed to achieve the goal in which the controller is able to simultaneously handle the constraints and maintain the compliant behavior. The design of NMPIC is the combination of a nonlinear model predictive control and impedance control based on the dynamics of the system. A disturbance observer is exploited to estimate the external wrench and then provide compensation for the model which was employed in the controller. Moreover, a weight adaptive strategy is proposed to perform the online tuning of the weighting matrix of the cost function within the optimal problem of NMPIC to improve the performance and stability. The effectiveness and advantages of the proposed method are validated by several simulations in different scenarios compared with the general impedance controller. The results also indicate that the proposed method opens a novel way for interaction force regulation.