Lindau is a surname. Notable people with the surname include:
Arvid Lindau (1892–1958), Swedish pathologist
Baruch Lindau (1759–1849), German-Jewish writer
Bill Lindau (1903–1989), American race car driver
Gustav Lindau (1866–1923), German botanist
Ingolf Lindau (born 1942), Swedish physicist
James H. Lindau, American politician, mayor of Bloomington, Minnesota, from 1977 to 1987
Karl Lindau, pen and stage name of Karl Gemperle (1853–1934), Austrian actor, writer and librettist
Märta Boman (1902–1986), née Lindau, Swedish politician
Paul Lindau (1839–1919), German writer, brother of the writer Rudolf Lindau
Peter Lindau (born 1972), Swedish footballer
Peeter Lindau (1886–?), Estonian politician
Rudolf Lindau (diplomat) (1829–1910), German writer
Rudolf Lindau (politician) (1888–1977), German politician and historian