An apparatus for injection molding an opening device on a sheet packaging material having a hole possessing an axis, formed through a first layer and sealed by a cover portion of a second layer; comprises a mold cavity coaxially housing the cover portion and comprising a first chamber adapted to be filled with molten plastic material on a first side of the cover portion, and a second tubular chamber projecting along the axis from the first chamber and adapted to be filled with the molten plastic material coming from the first chamber through an annular peripheral portion of the cover portion to form, on a second side of the cover portion, a spout; an annular rib delimiting a passage connecting the first and second chamber and defining, when filled with the plastic material, an annular tearable membrane connection portion between the spout and the plastic material covering the cover portion.