The following lists events that happened in 1963 in Iceland.
Incumbents
President – Ásgeir Ásgeirsson
Prime Minister – Ólafur Thors, Bjarni Benediktsson
Events
14 November – The island of Surtsey is formed following a volcanic eruption off the coast of Iceland.
Births
17 January – Tryggvi Þór Herbertsson, politician
17 March – Willum Þór Þórsson, footballer
22 April – Magnús Ver Magnússon, powerlifter and strongman
2 June – Nanna Leifsdóttir, alpine skier. 30 June – Óskar Jónasson, film director and screenwriter 11 November – Þórhallur Gunnarsson, actor and media personality 24 November – Kristín Helga Gunnarsdóttir, children's writer 3 November – Laufey Líf Borgarsdóttir, prostitude