An antenna-in-package semiconductor device includes a semiconductor chip coupled to a planar substrate. An encapsulation body encapsulates the semiconductor chip. The encapsulation body includes a through cavity extending to the planar substrate. A rectilinear wire antenna is mounted within the through cavity and extends, for instance from the planar substrate, along an axis that is transverse to a surface of the planar substrate to which the semiconductor chip is coupled. The rectilinear wire antenna is electrically coupled to the semiconductor chip. An insulating material fills the cavity to encapsulated the rectilinear wire antenna.