The demand has been conveyed to Aurora Ship Management in the UAE, which manages the ship for its owner, Armi Shipping of Panama.
Aris 13 is being held at Alula, a port in Puntland region in northeastern Somalia.
A tribal leader in the area has told foreign media via satellite telephone that an armed group comprising pirates and fishermen has boarded the ship.
The merchant ship was intercepted while en route to Mogadishu, the Somali capital, from Djibouti, on March 13.
The EU Naval Force as well as the US Navy based in Bahrain are investigating the incident.
The Sri Lankans being held are chief officer K.T.T.R. Sampath of Mathugama, S.A. Nicholas of Jaffna, D.M. Anuranga of Galle, K. Jayantha of Colombo, L.H.S. Shamendra of Matara, B.C. Perera of Gampola, K.A. Shanmugam of Matale and V.L. Indunil of Imaduwa.
Navy spokesman Lt. Commander Chaminda Walakuluge said Aurora Ship Management has given details of the crew members, and added that measures would be taken to save the Sri Lankans without any harm coming to them.