- Jan 1 Roswell B. Mason, Mayor of Chicago, dies at 86
- Jan 2 Frederick William Barber, South African frontiersman and scientist, dies at 78
- Jan 2 George Biddell Airy, English mathematician and 7th Astronomer Royal, dies at 90
- Jan 7 Ernst Wilhelm von Brücke, German physician and physiologist, dies at 72
- Jan 7 Muḥammad Tawfīq Pasha, Khedive of Egypt (1879-92), dies at 39
- Jan 8 Johannes Heykamp, Dutch Old-Catholic archbishop of Utrecht (The Decalaryion of Utrecht), dies at 67
- Jan 10 Heinrich Dorn, German composer and opera conductor, dies at 91
- Jan 13 Charles Albert White, American composer, dies at 62
- Jan 14 Henry Edward Manning, English Roman Catholic Cardinal (Archbishop of Westminster 1865-92), dies at 83
- Jan 14 Prince Albert Victor, Duke of Clarence, British prince (b. 1864)
- Jan 16 Imakita Kosen, Zen teacher/abbot of Engagkuji monastery, dies
- Jan 17 Alexandre Levy, Brazilian composer and pianist, dies at 27
- Jan 18 Anton Anderledy, Swiss Superior General of the Society of Jesus (b. 1819)
- Jan 21 John Couch Adams, English astronomer (co-discover Neptune), dies at 72
- Jan 22 Joseph Philo Bradley, U.S. Supreme Court Justice (b. 1813)
- Jan 31 Charles Spurgeon, English preacher and evangelist, dies at 57