- 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 A H von Waldeck, brother of queen Emma/last ruler of Waldeck
- Jan 22 Friedrich Paschen, German physicist
- Jan 28 Lala Lajpat Rai, Indian freedom fighter (d. 1928)
- Jan 28 Kaarlo Juho Ståhlberg, first president of Finland (d. 1952)
- Jan 30 Samuel Pierre l'Honoré Naber, Dutch rear-admiral and librarian, born in Zwolle, Netherlands (d. 1936)
- 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)
- Jan 31 Shastriji Maharaj, Indian spiritual leader (d. 1951)