Speaking to Italian media on a trip to Cyprus, the minister said the hospital would be established in the city of Misrata following a request from the country's UN-backed Government of National Accord (GNA).
Italian daily La Repubblica said the operation would involve 100 medical staff as well as 200 paratroopers, who would help set it up and then provide the security.
Details of the operation are expected to be confirmed when Gentiloni and Defence Minister Roberta Pinotti appear before a parliamentary defence committee on Tuesday.
Italy has already helped evacuate and treat a number of GNA-loyal fighters who suffered serious injuries during a recent offensive against Islamic State jihadists in the city of Sirte.
As well as trying to eliminate the IS contingent in Sirte, the GNA is facing a new challenge to its authority from a rival administration based in the east of the country and backed by military strongman General Khalifa Haftar.
Forces operating under Haftar on Monday took control of a key Mediterranean oil port, after seizing two others at the weekend.
The move has raised fears Libya could be on the verge of a new cycle of conflict.
Analysts say Haftar is taking advantage of the GNA forces being exhausted by their efforts against Isis.