We present a multiwavelength study of the field containing the unidentified X-ray source AX J1639.0-4642, discovered with the ASCA observatory and recently detected with the IBIS telescope, onboard the INTEGRAL satellite, dubbed IGR J16393-4643. The huge hydrogen column density towards the source, the hard spectral index in the 0.7-10 keV band and its flux variability suggest that the source is a High Mass X-ray Binary (HMXB) enshrouded by dust. Our search reveals the presence of a non-thermal radio counterpart within the X-ray error box. After a study of the broadband emission from X-rays to the radio domain, we propose that AX J1639.0-4642 is a dust-enshrouded Microquasar (MQ) candidate. In addition, the X-ray source is well within the 95% location contour of the unidentified gamma-ray source 3EG J1639-4702. The main properties of AX J1639.0-4642/3EG J1639-4702 are consistent with those of two other MQs previously proposed to display high-energy gamma-ray emission.