When modeling dynamical systems with uncertainty, one usually resorts to stochastic calculus and, specifically, Brownian motion. Recently, we proposed an alternative approach based on time-evolution of measures, called Measure Differential Equations, which can be seen as natural generalization of Ordinary Differential Equations to measures. The approach allows to pass to the limit in discrete approximations and attain finite-speed diffusion, concentration and other phenomena. In this paper we start building the theory of Measure Differential Inclusions which are the counterpart of Differential Inclusions for measures. We provide the general definitions and prove existence of solutions under continuity and convexity properties.