In a multi-cylinder internal combustion engine, provided with a system for variable actuation of the intake valves of the engine, the fuel injector (I) associated to each engine cylinder is surrounded by a sealing casing (57) which is part of a support body (19A-D; 70). The support body (19A-D; 70) is mounted on the engine cylinder head with the interposition of a support (50) surmounting the head and defining the seat in which the camshaft (11) is received and it defines a sealing peripheral edge cooperating with a sealing cover (58) which is mounted on the cylinder head. The cover (58) has a general base plane sealingly mounted on the cylinder head or on the support (50). The sealing peripheral edge of each sealing casing (57) is arranged in a parallel plane and raised with respect to the general base plane of the cover (58).