It is described a method and an apparatus for injection co-mould and assemble plastic material objects having a first part provided with a hinge pin, and a second part provided with an annular element suitable to be coupled in an articulated manner. The apparatus includes a mould having separated moulding impressions for the two parts to be moulded; a first moulding pin element defining the pin impression and a second moulding pin element defining the annular element impression are provided. The apparatus includes cooling means; particularly the first pin element is internally provided with a channel and a tubular element, being coaxially arranged and defining a cooling gap. A cooling fluid flows through the tubular element and the gap. Cams are provided which axially move the pin elements to cause the automatic assembly of the object during the mould opening and then to allow extracting the moulded object.