Abstract As part of our massive spectroscopic survey of 25 Galactic globular clusters with MUSE, we performed multiple epoch observations of NGC 3201 with the aim of constraining the binary fraction. In this cluster, we found one curious star at the main-sequence turn-off with radial velocity variations of the order of 100 km s− 1, indicating the membership to a binary system with an unseen component since no other variations appear in the spectra. Using an adapted variant of the generalized Lomb–Scargle periodogram, we could calculate the orbital parameters and found the companion to be a detached stellar-mass black hole with a minimum mass of 4.36 ± 0.41 M⊙. The result is an important constraint for binary and black hole evolution models in globular clusters as well as in the context of gravitational wave sources.