- Jan 1 Giuseppe Ferrata, Italian composer and pianist, born in Gradoli, Italy (d. 1928)
- Jan 3 Henry Lytton, British actor and opera singer (The Mikado), born in London, England (d. 1936)
- Jan 5 Julio Garavito Armero, Colombian astronomer, born in Bogotá, Colombia (d. 1920)
- Jan 10 Mary Ingalls, sister of American author Laura Ingalls Wilder, born in Pepin County, Wisconsin (d. 1928)
- Jan 13 Princess Marie of Orléans (d. 1908)
- Jan 17 Gen Sir Charles Fergusson, Governor-General of New Zealand (d. 1951)
- Jan 20 Friedrich, German prince, last ruler of Waldeck and Pyrmont, born in Arolsen, Waldeck and Pyrmont (d. 1946)
- Jan 22 Friedrich Paschen, German physicist (Paschen series), born in Schwerin, Mecklenburg-Schwerin (d. 1947)
- Jan 23 Benjamin Delmonte, Dutch theater director & actor (Black Haired Whore), born in Amsterdam, Netherlands (d. 1944)
- Jan 28 Kaarlo Juho Ståhlberg, first president of Finland (d. 1952)
- Jan 28 Lala Lajpat Rai, Indian freedom fighter (d. 1928)
- Jan 30 Samuel Pierre l'Honoré Naber, Dutch rear-admiral and librarian, born in Zwolle, Netherlands (d. 1936)
Henri Desgrange (1865-1940)
Jan 31 French cyclist, journalist and founder of the Tour de France, born in Paris, France
- Jan 31 Shastriji Maharaj, Indian spiritual leader (d. 1951)
- Jan 31 Tikhon of Moscow [Vasily Ivanovich Bellavin], 11th Patriarch of Moscow and all of Russia, born in Toropets District, Pskov, Russian Empire (d. 1925)