A rigid needle protector (10) comprising an inner part made from elastic material (11) and a rigid outer body (12) fixed to said inner part made of elastic material (11) by means of a turn up (121) of the lower axial end of said rigid outer body (12) said turn up (121) extending radially inwards from the peripheral outer surface (125) of said rigid outer body (12) the outer surface of said turn up (121) forming at the lower and radially outer axial edge thereof a sharp acute angle with respect to the peripheral outer surface (125) of said rigid outer body (12).
