The year 1645 in music involved some significant events.

• Juan Hidalgo de Polanco becomes leader of the chamber musicians at Spain's royal court.

• Giovanni Battista Abatessa – Intessatura di varii fiori..., a collection of guitar music, published in Naples

• Girolamo Frescobaldi – Canzoni alla francese, a posthumous print
• Cornelis Thymanszoon Padbrué - 't Lof Jubals, Op. 4, a collection of madrigals and motets

• Giovanni Faustini – Doriclea

• February 9 – Johann Aegidus Bach, organist and conductor (died 1716)
• February 22 (twins)
  • Johann Ambrosius Bach, musician (died 1695)
  • Johann Christoph Bach, musician (died 1693)
• November 30 – Andreas Werckmeister, organist and composer (died 1706)

• April 16 – Tobias Hume, soldier, viol player and composer (born c.1569)
• September 24 – William Lawes, English composer (born 1602)
• date unknown – William Smith, composer (born 1603)