The following lists events that happened during 1937 in the Union of Soviet Socialist Republics.

• General Secretary of the Communist Party of the Soviet Union — Joseph Stalin
• Chairman of the Central Executive Committee of the Congress of Soviets — Mikhail Kalinin
• Chairman of the Council of People's Commissars of the Soviet Union — Vyacheslav Molotov

• January 23–30 — Trial of the Anti-Soviet Trotskyist Center
• June — Case of Trotskyist Anti-Soviet Military Organization
• June 18–20 — The first transpolar flight and the first non-stop USSR-USA flight [ru] by the crew led by Valery Chkalov
• July 12–14 — A world-record non-stop flight [ru], by the crew led by Mikhail Gromov, from Moscow to San Jacinto, California
• December 12 — Soviet Union legislative election, 1937

• Bezhin Meadow — directed by Sergei Eisenstein
• Lullaby — directed by Dziga Vertov
• The Return of Maxim — directed by Grigori Kozintsev and Leonid Trauberg
• Without Dowry — directed by Yakov Protazanov

• January 2 — Marietta Chudakova, Soviet and Russian literary critic (d. 2021)
• January 12 — Mikheil Meskhi, footballer (d. 1991)
• January 20 — Mintimer Shaimiev, 1st Head of Tatarstan
• January 30 — Boris Spassky, Soviet and Russian chess grandmaster
• February 16 — Yuri Manin, mathematician (d. 2023)
• February 19 — Boris Pugo, 9th Minister of Interior of the Soviet Union (d. 1991)
• February 25 — Yegor Stroyev, 2nd Chairman of the Federation Council
• February 28 — Vitaly Tulenev, Soviet and Russian painter, visual artist and art teacher (d. 1997)
• March 4 — Yuri Senkevich, Soviet and Russian physician and scientist (d. 2003)
• March 6 — Valentina Tereshkova, Soviet and Russian cosmonaut
• March 15 — Valentin Rasputin, Soviet and Russian writer (d. 2015)
• March 16 — Valentina Parshina, agronomist and politician (d. 2020)^[1]
• March 18 — Aleksei Zasukhin, Soviet and Russian boxer (d. 1996)
• March 23 — Boris Zaytsev, Soviet and Russian ice hockey goaltender (d. 2000)
• April 2 — Yuri Falin, Soviet and Russian football player (d. 2003)
• April 9 — Leonid Barbier, Soviet and Ukrainian swimmer (d. 2023)
• April 10 — Bella Akhmadulina, Soviet and Russian poet (d. 2010)
• April 13 — Osman Mirzayev, Head of Presidential Administration of Azerbaijan (d. 1991)
• April 14 — Anatoly Lysenko, television figure, journalist, director and producer (d. 2021)
• April 24 — Galina Semenova, Soviet and Russian politician (d. 2017)
• April 27 — Olga Bondareva, mathematician and economist (d. 1991)
• April 29 — Yevgeny Feofanov, boxer (d. 2000)
• May 1 — Hazret Sovmen, 2nd Head of the Republic of Adygea
• May 7 — Sergey Ling, 3rd Prime Minister of Belarus
• May 10 — Vadim Rogovin, Soviet and Russian Trotskyist historian and sociologist (d. 1998)
• May 30 — Aleksandr Demyanenko, actor (d. 1999)
• June 12 — Vladimir Arnold, mathematician (d. 2010)
• June 18 — Vitaly Zholobov, Soviet and Ukrainian cosmonaut
• July 2 — Oleg Shenin, politician (d. 2009)
• July 6 — Vladimir Ashkenazy, Soviet and Russian pianist
• July 7 — Valery Anisimov, wrestler
• July 8 — Lidia Klement, singer (d. 1964)
• July 21 — Eduard Streltsov, footballer (d. 1990)
• August 10 — Anatoly Sobchak, Mayor of Saint Petersburg (d. 2000)
• August 20 — Uzakbay Karamanov, last Chairman of the Council of Ministers of the Kazakh SSR (d. 2017)
• August 26 — Gennady Yanayev, Vice President of the Soviet Union (d. 2010)
• September 6 — Gennady Shpalikov, poet, screenwriter and film director (d. 1974)
• September 13 — Igor Ivanov, Acting Head of Karachay-Cherkessia (d. 2000)
• September 16 — Valentina Dimitrieva, Soviet and Russian farm worker (d. 2019)
• September 20 — Valentin Knysh, politician (d. 2022)
• September 23 — Aleksandr Medakin, Soviet and Russian football player (d. 1993)
• September 24 — Umyar Mavlikhanov, Soviet and Russian fencer (d. 1999)
• September 26 — Valentin Pavlov, 11th Premier of the Soviet Union (d. 2003)
• September 28 — Georgy Rerberg, Soviet and Russian cinematographer (d. 1999)
• September 30
  • Yuri Maslyukov, Soviet and Russian politician (d. 2010)
  • Vitaliy Boiko, Soviet and Ukrainian lawyer and diplomat (d. 2020)
• October 3 — Aleksandr Kondratov, Soviet and Russian linguist, biologist, journalist and poet (d. 1993)
• October 8 — Eduard Rossel, 1st Governor of Sverdlovsk Oblast
• October 27 — Victor Popov, Soviet and Russian theoretical physicist (d. 1994)
• November 6 — Vadim Bakatin, 8th Chairman of the Committee for State Security (d. 2022)
• November 12 — Alexey Obukhov, Russian diplomat and politician (d. 2022)
• November 13 — Mikhail Nikolayev, 1st Head of the Sakha Republic (d. 2023)
• November 22 — Nikolai Kapustin, Soviet and Russian composer and pianist (d. 2020)
• November 25 — Serikbolsyn Abdildin, 1st Chairman of the Supreme Council of Kazakhstan (d. 2019)
• November 26 — Boris Yegorov, Soviet and Russian physician and cosmonaut (d. 1994)
• November 29 — Ali Aliyev, Soviet and Russian freestyle wrestler (d. 1995)
• December 7 — Simon Gindikin, Russian mathematician
• December 24 — Viacheslav Chornovil, Soviet dissident and Ukrainian politician (d. 1999)

• 10 January – Martemyan Ryutin (born 1890)
• 30 January
  • Georgy Pyatakov (born 1890)
  • Nikolay Muralov (born 1877)
• 18 February – Grigory Ordzhonikidze (born 1886)
• 13 April – Ilya Ilf (born 1897)
• 31 May
  • Yan Gamarnik (born 1894)
  • Nikolai Uglanov (born 1886)
• 12 June
  • Mikhail Tukhachevsky (born 1893)
  • Ieronim Uborevich (born 1896)
  • Iona Yakir (born 1896)
  • Vitovt Putna (born 1893)
  • Vitaly Primakov (born 1897)
  • Robert Eideman (born 1895)
  • Maria Ulyanova, younger sister of Vladimir Lenin (born 1878)
• 13 July – Mikhail Alafusov (born 1891)
• 30 October – Avel Enukidze (born 1877)
• 26 November – Leonid Veyner (born 1897)
• 28 November – Ernest Appoga (born 1898)
• Vassily Ryutin, older son of Martemyan Ryutin, executed (born 1910)
• Vissarion Ryutin, younger son of Martemyan Ryutin, executed (born 1913)

• 1937 in fine arts of the Soviet Union
• List of Soviet films of 1937