Our understanding of strong gravity near supermassive compact objects has recently improved thanks to the measurements made by the Event Horizon Telescope (EHT). We use here the M87∗ shadow size to infer constraints on the physical charges of a large variety of nonrotating or rotating black holes. For example, we show that the quality of the measurements is already sufficient to rule out that M87∗ is a highly charged dilaton black hole. Similarly, when considering black holes with two physical and independent charges, we are able to exclude considerable regions of the space of parameters for the doubly-charged dilaton and the Sen black holes.