In this paper, we present a Perception-constrained Nonlinear Model Predictive Control (NMPC) framework for the real-time control of multi-rotor aerial vehicles. Our formulation considers both constraints from a perceptive sensor and realistic actuator limitations that are the rotor minimum and maximum speeds and accelerations. The formulation is meant to be generic and considers a large range of multi-rotor platforms (such as underactuated quadrotors or tilted-propellers hexarotors) since it does not rely on differential flatness for the dynamical equations, and a broad range of sensors, such as cameras, lidars, etc... The perceptive constraints are expressed to maintain visibility of a feature point in the sensor's field of view, while performing a reference maneuver. We demonstrate both in simulation and real experiments that our framework is able to exploit the full capabilities of the multi-rotor, to achieve the motion under the aforementioned constraints, and control in real-time the platform at a motor-torque level, avoiding the use of an intermediate unconstrained trajectory tracker.