The deal has been signed for a period of 30 years, the company said in a filing to the Zagreb bourse without elaborating further.
The three-star Hotel Bisevo is the only existing hotel in the town of Komiza, on the island of Vis.
It would be converted into a five-star hotel under the Marriott Autograph Collection brand thanks to an investment of 52 million euro ($51.8 million), according to information published on the Facebook page of the Komiza's tourism association earlier this month. It would be the first Marriott hotel in the Adriatic country.
Two funds run by Croatian pension fund management company PBZ CO control almost 93% of Modra Spilja among themselves.
Modra Spilja's shares last traded on July 13 on the Zagreb bourse, closing flat at 11.50 kuna.
(1 euro = 7.513 Croatian kuna)