A search is presented for the lepton flavour violating decay B+ → K+μ−τ+ using a sample of proton-proton collisions at centre-of-mass energies of 7, 8, and 13 TeV, collected with the LHCb detector and corresponding to a total integrated luminosity of 9 fb−1. The τ leptons are selected inclusively, primarily via decays with a single charged particle. The four-momentum of the τ lepton is determined by using B+ mesons from Bs2∗0→B+K− decays. No significant excess is observed, and an upper limit is set on the branching fraction ℬ(B+ → K+μ−τ+) < 3.9 × 10−5 at 90 % confidence level. The obtained limit is comparable to the world-best limit. [Figure not available: see fulltext.].