Claussøn is a Swedish surname. Notable people with the surname include:
Claudius Claussøn Swart (1388–?), Danish geographer and cartographer Ida Ekeroth Clausson (born 1991), Swedish politician Niels Claussøn Senning (c. 1580–1617), Danish/Norwegian Lutheran Bishop Peder Claussøn Friis (1545–1614), Norwegian clergyman, author, and historian