The Muon Collider is a possible option for the next generation of high energy collider machines. It would permit to achieve the energy frontier in lepton collisions, without occurring in significant synchrotron radiation losses as in electrons rings.
Among the technological challenges in the realization of such a machine, the treatment of the beam-induced background is one of the most critical issues for the detectors.
Beams with intensity of the order of $10^{12}$ muons per bunch are necessary to obtain the desired luminosity, therefore the muons decay rate is very high. Beam decay products and subsequent particles from secondary interactions with the machine elements can reach the interaction point, limiting the physical performance of the detector. A study of the beam-induced background is presented together with possible strategies for its reduction. Preliminary results on the reconstruction of a benchmark process, $\mu^+\mu^-\to H\nu\bar{\nu}\to b \bar{b}\nu\bar{\nu}$, including the beam-induced background are illustrated as demonstration of physics measurements feasibility in this harsh environment.