The device (1) comprises a steam generator (2, 4), a compressed-air generator (9, 11) and a dispensing wand (10) connected or adapted to be connected to the steam generator (2, 4) and the compressed-air generator (9, 11) and adapted to be introduced into a receptacle (R) containing the milk (M) to be heated and frothed. The dispensing wand (10) defines first and second conduits (21, 22) separate from each other and having respective separate inlets (10a, 10b) for connection to the steam generator (2, 4) and the compressed-air generator (9, 11), respectively, as well as respective separate outlets (10c, 23； 10d, 24) for dispensing during use a flow of steam and a low of compressed air, respectively, within the milk (M) contained in the receptacle (R), said outlets (23, 24) being arranged such that the flows of steam and compressed air exiting therefrom intersect each other.
