We present photometric and spectroscopic optical and near-infrared (NIR) observations taken during the outburst of the microquasar V4641 Sgr = SAX J1819.3 - 2525 in 1999 September. We observed an increase in the J-Ks colour between 5 and 8 d after the outburst, which we interpret as likely evidence for the presence of dust around the source. We also observed an extraordinarily strong, broad and variable Hα line, with a velocity width of 4560 km s-1, suggesting the presence of a high-velocity outflow component. We constrain the distance of the system between 3 and 8 kpc, locating it further away than previously derived from radio observations, but consistent with results from Orosz et al. We then discuss the nature of this system, showing that the companion star is either a B3-A2 main-sequence star or a B3-A2 subgiant crossing the Hertzsprung gap. The system is therefore an intermediate- or high-mass X-ray binary system (IMXB or HMXB). The distance derived by these optical/NIR observations implies that the jets observed by Hjellming et al. would then exhibit apparent velocities of ~10c. We finally discuss the possibility of an interaction between the jets and surroundings of the source, and also of this source being a `microblazar'.