Efficient excitation of nuclei via exchange of a real or virtual photon has a fundamental importance for nuclear science and technology development. Here, we present a mechanism of nuclear excitation based on the capture of a free muon into the atomic orbits (NEμC). The cross section of such a proposed process is evaluated using the Feshbach projection operator formalism and compared to other known excitation phenomena, i.e., photoexcitation and nuclear excitation by electron capture (NEEC), showing up to 10 orders of magnitude increase in cross section. NEμC is particularly interesting for MeV excitations that become accessible thanks to the stronger binding of muons to the nucleus. The binding energies of muonic atoms have been calculated introducing a state of the art modification to the Flexible Atomic Code. An analysis of experimental scenarios in the context of modern muon production facilities shows that the effect can be detectable for selected isotopes. The total probability of NEμC is predicted to be P≈1×10^{-6} per incident muon in a beam-based scenario. Given the high transition energy provided by muons, NEμC can have important consequences for isomer feeding and particle-induced fission.