Otto Fabricius was born in Rudkøbing on the island of Langeland, Denmark where his father was a rector. In his youth, he was largely educated at home by tutors. In 1762, he was matriculated at the University of Copenhagen. In 1765, he was admitted to the Greenland Mission Seminary (Seminarium Groenlandicum) where he attended classes taught by Poul Egede. In 1768 he graduated with a degree in divinity.
He was sent as a missionary to the southwestern coast of Greenland from 1768–1773. During this period, he made enormous amounts of observations and collections. The facilities at his command were primitive to the extreme. His laboratory was an Inuit house made of turf. His only artificial light was an oil lamp. He had a few magnifying glasses and only one book was in his library, LinnaeiSystema Naturae by Carolus Linnaeus. Nevertheless, he made enough zoological observation to be able to publish Fauna Groenlandica (1780), which was written in Latin, after his return to Denmark. Here, he described 473 animal species, 130 of which were new to science. Detailed descriptions are given, including information on habitat and behaviour, the vernacular Inuit name, what use inuit people make of the animal and not least how they caught or trapped it. 
In 1774, he was appointed rector at Drangedal in Telemark, Norway where he stayed until 1779 while he completed work for a Greenlandic language dictionary which was published in 1804. In 1789, he succeeded Poul Egede to become a lecturer in the Greenland Mission Seminary. In 1818, he was appointed an Honorary Bishop of the Church of Denmark and awarded a Doctorate of Divinity.