The statement from the office of the president say that eight accused were sentenced for committing an act of piracy and three others for aiding and abetting an act of piracy.
The Seychelles said the sentences marked the first time it has prosecuted and convicted pirates.
Another 29 suspected and accused Somali pirates are still pending trial in the Seychelles or awaiting transfer to Somalia.
In June, the United Nations built a new court for pirates in Kenya with contributions from Australia, Canada, the European Union, Germany and the United States.
Kenya has 123 prisoners in custody. Eighteen pirates have been tried and convicted.
Pirates based in neighboring Somalia have made the Gulf of Aden one of the world's most dangerous shipping lanes.