Events from the year 1637 in art.

• October 13 – English Royal Navy first-rate ship of the line Sovereign of the Seas is launched at Woolwich Dockyard at a cost of £65,586, adorned from stern to bow with gilded carvings after a design by Anthony van Dyck.
• Claude Lorrain produces a series of etchings of a display of fireworks in Rome.
• Nicolas Poussin begins to paint the first series of Seven Sacraments.

• 
  de Grebber, Elisha
• 
  Claude, Seaport

• Cornelis de Baellieur
  • Interior of an Art Gallery
• Claude Lorrain
  • Landscape with a Country Dance
  • Seaport (Villa Medici)
• Pieter de Grebber – Elisha refusing the gifts of Naaman
• Rembrandt – A Polish Nobleman
• Anthony van Dyck – Prince Rupert of the Rhine (approximate date)

• Bernini – Bust of King Charles I of England

• March 5 – Jan van der Heyden, painter, printmaker and inventor (died 1712)
• April 16 – Jean-Jacques Clérion, French sculptor (died 1714)
• June 25 – Christophe Veyrier, French sculptor (died 1689)
• December 12 – Cesare Gennari, Italian painter (died 1688)
• date unknown
  • Abraham Begeyn, Dutch painter of landscapes and cattle (died 1697)
  • Niccolò Berrettoni, Italian painter (died 1682)
  • Francesco Bonifaccio, Italian painter (d. unknown)
  • Sigismondo Caula, Italian painter (died 1724)
  • Andrea Celesti, Venetian painter (died 1712)
  • Martin Desjardins, French sculptor and stuccoist of Dutch birth (died 1694)
  • Carl Ferdinand Fabritius, German painter (died 1673)
  • Vicente Salvador Gómez, Spanish Baroque painter (died 1678)
  • Giovanni Marracci, Italian painter (died 1704)
  • Giovanni Moneri, Italian painter (died 1714)
  • Pieter Mulier II, Dutch Golden Age painter (died 1701)
  • Michelangelo Palloni, Italian painter (died 1712)
  • Niccola Ricciolini, Italian painter (d. unknown)
  • Girolamo Troppa – Italian painter of the Baroque (died 1710)

• January 3 - Daniel Rabel, French painter, engraver, miniaturist, botanist and natural history illustrator (born 1578)
• March 6 - Crispijn van de Passe the Elder, Dutch publisher and engraver (born 1564)
• July 12 – Willem van Haecht, Flemish painter (born 1593)
• September 14 – Theodoor Rombouts, Flemish painter (born 1597)
• December 27 – Vincenzo Giustiniani, art collector, patron of Caravaggio (born 1564)
• date unknown
  • Honami Kōetsu, Japanese craftsman, founder of the Rinpa school (born 1558)
  • Diego de Leyva, Spanish religious painter (born c. 1580)
  • Willem de Passe, Dutch engraver and designer of medals (born 1598)
  • Arent Passer, stonemason and architect (born c. 1560)
  • Domenico Robusti, painter (born 1562)
  • Cornelis Verbeeck – Dutch painter of the Baroque period (born 1590)