The destroyer Iris Dena, with a crew of 180, made a distress call early in the morning from an area just outside Sri Lankan territorial waters.
Sri Lanka's navy and air force responded and rescued around 30 people, Foreign Minister Vijatha Herath says.
It is not clear what happened to the ship. Injured crew members are being taken to a hospital in Galle, Sri Lanka.
An opposition politician asked the government in parliament whether the ship had been bombed as part of the war raging in Iran. The government did not give a straight answer to that question.
