• Monarch – Christian X^[1]
• Prime minister – Thorvald Stauning

Football edit

• B 1903 wins their fourth Danish football championship by winning the 1937–38 Danish Championship League,

Swimming edit

• 6–13 August Denmark wins five gold medals, one silver medal and one bronze medal at the 1938 European Aquatics Championships.

January–March edit

• 27 January – Povl Dissing, singer (died 2022)

April–June edit

• 25 May – John Olsen, artist (died 2019)

July– September edit

• 12 July – Lars Hillingsø, fashion designer (died 2005)
• 18 July – Erik Wedersøe, actor (died 2011)
• 1 September – Per Kirkeby, painter, sculptor (died 2018)

October–December edit

• 11 October – Merete Ries, publisher (died 2018)^[2]
• 15 November – Henning Camre, cinematographer, film industry administrator
• 27 November – Marianne Grøndahl, photographer (died 2012)

January–March edit

• 3 February – Niels Skovgaard, artist (born 1958)
• 10 February – Valdemar Irminger, painter (born 1859)

April–June edit

• 4 April – Alfred Schmidt, painter (born 1858)
• 16 April – Karl Madsen, art historian, painter and arts administrator (born 1855)
• 9 May – Thomas B. Thrige, businessman (born 1866)

July–September edit

• 2 July – Lau Lauritzen Sr., film director, screenwriter and actor (born 1878)

October–December edit

• 22 December – Johannes Wilhjelm, painter (born 1868)