- Jan 3 James Merritt Ives, American lithographer with Nathaniel Currier (b. 1824)
- Jan 4 Manuel Pavía y Rodríguez de Alburquerque, Spanish general, dies at 66
- Jan 9 Aaron Lufkin Dennison, American watch manufacturer (b. 1812)
- Jan 10 Benjamin Louis Paul Godard, composer, dies at 45
- Jan 22 Edward Solomon, English composer, dies at 39
- Jan 24 Lord Randolph Churchill, British politician (b. 1849)
- Jan 26 Arthur Cayley, mathematician, dies
- Jan 28 François Certain Canrobert, French marshal and parliament member, dies at 85