Studies of young clusters have shown that a large fraction of O-/early B-type stars are in binary systems, where the binary fraction increases with mass. These massive stars are present in clusters of a few Myr, but gradually disappear for older clusters. The lack of detailed studies of intermediate-age clusters has meant that almost no information is available on the multiplicity properties of stars with M < 4M_⊙⁠. In this study we present the first characterization of the binary content of NGC 1850, a 100 Myr-old massive star cluster in the Large Magellanic Cloud, relying on a VLT/MUSE multi-epoch spectroscopic campaign. By sampling stars down to M = 2.5 M_⊙, we derive a close binary fraction of 24 ± 5 per cent in NGC 1850, in good agreement with the multiplicity frequency predicted for stars of this mass range. We also find a trend with stellar mass (magnitude), with higher mass (brighter) stars having higher binary fractions. We modelled the radial velocity curves of individual binaries using THE JOKER and constrained the orbital properties of 27 systems, ∼17 per cent of all binaries with reliable radial velocities in NGC 1850. This study has brought to light a number of interesting objects, such as four binaries showing mass functions f(M) > 1.25 M_⊙. One of these, star #47, has a peculiar spectrum, explainable with the presence of two discs in the system, around the visible star and the dark companion, which is a black hole candidate. These results confirm the importance and urgency of studying the binary content of clusters of any age.