Mucke or Mücke or Muecke is a German surname. Notable people with the surname include:
Elli Mücke (born 1981), German singer
Hermann Mucke (bioscientist) (born 1955), Austrian bioscientist and consultant
Hermann Mucke (astronomer) (born 1935), Austrian astronomer and public educator
Manuela Mucke (born 1975), German sprint canoer
Stefan Mücke (born 1981), German racing driver
Charles Andrew Muecke (1918–2007), US federal judge
Hugo Carl Emil Muecke (1842–1929), Australian politician
Stephen Muecke, Australian linguist