Year 1513 (MDXIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.
- July 22 – Christian II becomes King of Denmark and Norway.
- August 16 – Battle of Dubica (part of the Hundred Years' Croatian–Ottoman War): Croatian troops under Petar Berislavić, Ban (Viceroy) of Croatia, defeat an Ottoman army under Sanjak-bey Junuz-aga
- August 16 – Battle of the Spurs (or Battle of Guinegate, part of the War of the League of Cambrai): English and allied troops under Henry VIII defeat French cavalry under Marshal La Palice.
- August 22 – Thérouanne is captured by Henry VIII of England.
- September – The dispute between Johann Reuchlin and Johannes Pfefferkorn relative to the Talmud and other Jewish books, is referred to Pope Leo X.
- September 9 – Battle of Flodden: King James IV of Scotland is defeated and killed by an English army under Thomas Howard, Earl of Surrey. James's son, the Duke of Rothesay, becomes James V, King of Scots.
- September 25 – Vasco Núñez de Balboa, "silent upon a peak in Darién", first sees what will become known as the Pacific Ocean.
- October 7 – Battle of La Motta (War of the League of Cambrai): Spanish troops under Ramón de Cardona and Fernando d'Avalos decisively defeat those of the Republic of Venice under Bartolomeo d'Alviano on Venetian territory.
- February 14 – Domenico Ferrabosco, Italian composer (d. 1573)
- March 15 – Hedwig Jagiellon, Electress of Brandenburg (d. 1573)
- April 22 – Tachibana Dōsetsu, Japanese Daimyo (d. 1585)
- June 10 – Louis, Duke of Montpensier (1561–1582) (d. 1582)
- August 3 – John, Margrave of Brandenburg-Küstrin (d. 1571)
- September 23 – Hans Buser, Swiss noble (d. 1544)
- September 24 – Catherine of Saxe-Lauenburg, queen of Gustav I of Sweden (d. 1535)
- October 30 – Jacques Amyot, French writer (d. 1593)
- December 3 – Lorenzo Strozzi, Italian Catholic cardinal (d. 1571)
- December 23 – Thomas Smith, English scholar and diplomat (d. 1577)
- date unknown
- probable – Elizabeth Seymour, English noble, sister-in-law of Henry VIII of England (d. 1563)
- January – Hans Folz, German author (b. c. 1437)
- January 20 – Helena of Moscow, Grand Duchess consort of Lithuania and queen consort of Poland (b. 1476)
- February 20 – King John of Denmark, Norway, and Sweden (b. 1455)
- February 21 – Pope Julius II (b. 1443)
- March 10 – John de Vere, 13th Earl of Oxford, English general (b. 1443)
- April 24 – Şehzade Ahmet, oldest son of Sultan Bayezid II (executed) (b. 1465)
- April 30 – Edmund de la Pole, 3rd Duke of Suffolk, Duke of Suffolk (b. 1471)
- August 3 – Ernst II of Saxony, Archbishop of Magdeburg (1476–1513) and Administrator of Halberstadt (b. 1464)
- September 9 (killed at the Battle of Flodden)
- James IV of Scotland (b. 1473)
- George Douglas, Master of Angus (b. 1469)
- William Douglas of Glenbervie (b. 1473)
- William Graham, 1st Earl of Montrose, Scottish politician (b. 1464)
- George Hepburn, Scottish bishop
- Adam Hepburn, 2nd Earl of Bothwell, Scottish politician, Lord High Admiral of Scotland
- Adam Hepburn of Craggis
- David Kennedy, 1st Earl of Cassilis, Scottish soldier (b. 1478)
- Alexander Lauder of Blyth, Scottish politician
- Alexander Stewart, Scottish archbishop (b. 1493)
- Matthew Stewart, 2nd Earl of Lennox, Scottish politician (b. 1488)
- October 27 – George Manners, 11th Baron de Ros, English nobleman
- date unknown
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