Steinunn may refer to:

• Ragnhildur Steinunn Jónsdóttir (born 1981), Icelandic television personality, actress, and former Ms. Iceland
• Steinunn Ólína Þorsteinsdóttir, Icelandic actress, writer and producer
• Steinunn Finnsdóttir (c. 1640 – c. 1710), Icelandic poet
• Steinunn Kristín Þórðardóttir (born 1972), Managing Director of Glitnir Bank in London, UK
• Steinunn Refsdóttir, Icelandic skaldic poetic active at the end of the 10th century
• Steinunn Sigurðardóttir (born 1950), Icelandic author
• Steinunn Sigurðardóttir (fatahönnuður), Icelandic fashion designer
• Steinunn Valdís Óskarsdóttir (born 1965), Icelandic politician, and a former mayor of Reykjavík