We observed the accreting millisecond pulsar SAX J1808.4−3658 with Gemini-South in g′ and i′ bands, nearly simultaneous with XMM–Newton observations. A clear periodic flux modulation on the system's orbital period is present, consistent with the varying aspect of the donor star's heated face. We model the contributions of a disc and donor star to these optical bands. To produce the observed modulation amplitudes, we conclude that the donor must be irradiated by an external flux two orders of magnitude greater than provided by the measured X-ray luminosity. A possible explanation for this irradiation is that the radio pulsar mechanism becomes active during the quiescent state as suggested by Burderi et al., with relativistic particles heating the donor's day side face. Our modelling constrains the binary inclination to be 36°–67°. We obtain estimates for the pulsar mass of >2.2 M⊙ (although this limit is sensitive to the source's distance), consistent with the accelerated neutron star cooling in this system indicated by X-ray observations. We also estimate the donor mass to be 0.07–0.11 M⊙, providing further indications that the system underwent non-standard binary evolution to reach its current state.