Henrik Olrik, born in Copenhagen, was son of customs inspector Henrik Johan Ludvig Olrik and Benedicte Martinette (née Heiberg).
Olrik was admitted to Royal Danish Academy of Fine Arts in 1844 where he initially studied sculpture under Herman Wilhelm Bissen, while in the same time working at the Royal Copenhagen Porcelain Factory, where he made reduced copies of Bertel Thorvaldsen works. He graduated from the Academy in 1851 after winning two silver medals for his works in 1848 and 1851.
In 1854 Olrik went to Paris pursue his painting interests. He studied in the studio of Thomas Couture and had his first painting exhibition in 1855.
After returning to Denmark in 1855, Olrik soon became recognized as a reputable portrait painter and painted portraits of a wide variety of individuals including King Christian IX of Denmark, his daughter Alexandra - (later the Princess of Wales), members of the Danish Parliament and representatives of Danish and Scandinavian high society, including Sigurd Ibsen and Henrik Ibsen.