The present invention relates to a package for containing a product comprising a support (1) which has: a base (2) configured for receiving one or more products, a perimetral edge (6) which surrounds the base (2), a removable portion (21) extending as a prolongation of the perimetral edge (6) away from the base (2). The package further comprises a closing film (10) engaged to a portion of the perimetral edge (6) and to the removable portion (21) and configured for defining—in cooperation with the support (1)—a housing compartment (5) for the product (P); the removable portion (21) and at least a part of the closing film (10) are configured for being separated from the support (1) during an opening step of the package (100). The package (100) is configured for defining a closing condition in which: the closing film in cooperation with the support (1) prevents access to the housing compartment (5) of the product (P), and the removable portion (21) is aligned with at least a portion (6a) of the perimetral edge (6) from which it extends as a prolongation. The package (100) further comprises a gripping portion (22) emerging from the perimetral edge 6 and extending, in the closed condition of the package, transversally to the removable portion (21). The present invention also relates to a process and an apparatus for making said package.