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Abstract The Muon Collider is one of the most promising future collider facilities with the potential to reach multi-TeV center-of-mass energy and high luminosity. Due to the significant Higgs boson production cross section in muon-antimuon collisions at such high energies, the collider offers an excellent opportunity for in-depth exploration of Higgs boson properties. It holds the capability to significantly advance our understanding of the Higgs sector to a very high level of precision. However, the presence of beam-induced background resulting from the decay of the beam muons poses unique challenges for detector development and event reconstruction. In this paper, the prospects for measuring various Higgs boson properties at a center-of-mass energy of 3 TeV are presented, using a detailed detector simulation in a realistic environment. The study demonstrates the feasibility of achieving high precision results with the current state-of-the-art detector design. In addition, the paper discusses the detector requirements necessary to achieve this level of accuracy.