An apparatus for packaging a product arranged on a tray, said apparatus comprising a packaging assembly configured for tightly fixing a film (10; 18) to one or more trays, the packaging assembly including a prefixed number of seats configured for receiving said one or more trays, wherein: - each of said seats presents a mouth peripherally delimited by an abutment surface, each of said seats being configured to receive at least one respective tray with a flange of each tray resting on the abutment surface of the respective seat, and - the packaging assembly defines - in correspondence of each of said seats - a number of first apertures configured to inject gas towards the inside of the respective seat, wherein each of said first apertures is positioned in correspondence of the mouth of the respective seat and extends above said abutment surface; wherein the packaging assembly includes, for each of said seats, a number of second apertures located on a side of the seat opposite with respect to the first aperture(s); wherein the packaging assembly further comprises: - a lower tool defining the prefixed number of seats and hosting a number of first conduits, wherein the first conduits present terminal edges delimiting said first apertures such that each of said first apertures presents at least a major portion extending above the abutment surface of the respective seat; - an upper tool facing the lower tool, at least the upper and lower tools (21; 22) cooperating to define a packaging chamber; and - a control unit connected to the packaging assembly and configured for commanding the packaging assembly to pass from a first operating condition, where said packaging chamber is open to receive the film (10; 18), and a second operating condition, where said packaging chamber is closed, optionally hermetically closed; wherein the lower tool first conduits have an end, terminating in said terminal edges defining said first apertures, and an opposite end, in fluid communication with a gas supply circuit; wherein the lower tool comprises a number of second conduits having an end, terminating in said second apertures, and an opposite end, in fluid communication with a gas evacuation circuit, characterized in that each of said first apertures is positioned in correspondence of corner regions of the mouth of the respective seat. - each of said seats presents a mouth peripherally delimited by an abutment surface, each of said seats being configured to receive at least one respective tray with a flange of each tray resting on the abutment surface of the respective seat, and - the packaging assembly defines - in correspondence of each of said seats - a number of first apertures configured to inject gas towards the inside of the respective seat, wherein each of said first apertures is positioned in correspondence of the mouth of the respective seat and extends above said abutment surface; - a lower tool defining the prefixed number of seats and hosting a number of first conduits, wherein the first conduits present terminal edges delimiting said first apertures such that each of said first apertures presents at least a major portion extending above the abutment surface of the respective seat; - an upper tool facing the lower tool, at least the upper and lower tools (21; 22) cooperating to define a packaging chamber; and - a control unit connected to the packaging assembly and configured for commanding the packaging assembly to pass from a first operating condition, where said packaging chamber is open to receive the film (10; 18), and a second operating condition, where said packaging chamber is closed, optionally hermetically closed;