We present theoretical calculations of the optical spectrum of monolayer MoS2 with a charged defect. In particular, we solve the Bethe–Salpeter equation based on an atomistic tight-binding model of the MoS2 electronic structure which allows calculations for large supercells. The defect is modelled as a point charge whose potential is screened by the MoS2 electrons. We find that the defect gives rise to new peaks in the optical spectrum approximately 100–200 meV below the first free exciton peak. These peaks arise from transitions involving in-gap bound states induced by the charged defect. Our findings are in good agreement with experimental measurements.