The 1978 Milan Indoor, also known by its sponsored name Ramazzotti Cup, was a men's tennis tournament played on indoor carpet courts at the Palazzo dello Sport in Milan in Italy.

The event was part WCT Tour which was incorporated into the 1978 Colgate-Palmolive Grand Prix circuit.

It was the inaugural edition of the tournament and was held from 27 March through 2 April 1978.

Second-seeded Björn Borg won the singles title.

[5] Björn Borg defeated Vitas Gerulaitis 6–3, 6–3 José Higueras / Víctor Pecci defeated Wojciech Fibak / Raúl Ramírez 5–7, 7–6, 7–6