We study the properties ofK * mesons in nuclear matter using a unitary approach in coupled channels within the framework of the local hidden gauge formalism and incorporating theKπ decay channel in matter. The in-mediumK * N interaction accounts for Pauli blocking effects and incorporates theK * self-energy in a self-consistent manner. We also obtain theK * (off-shell) spectral function and analyze its behavior at finite density and momentum. At a normal nuclear matter density, theK * meson feels a moderately attractive potential, while theK * width becomes five times larger than in free space. We estimate the transparency ratio of the γ A → K + K * − A reaction, which we propose as a feasible scenario at the present facilities to detect changes in the properties of theK * meson in nuclear medium.