He was born in Skógar in Þorskafjörður, western Iceland, into a poor family. He studied theology, was ordained priest and for a number of years served as pastor at Oddi, S Iceland, and later in Akureyri. He also worked as a newspaper editor and schoolteacher. In his religious views, Matthías leaned towards Unitarianism. Matthías made some trips to the continent to further his education.
Intending to become a businessman, Matthías discovered his passion for languages and literature. In addition to his own works, which include many hymns, Matthías was a prolific translator, especially from English and the Scandinavian languages. His translations from Shakespeare include Hamlet, Macbeth, Othello and Romeo and Juliet.
Matthías's popular comedy, "Skugga-Sveinn", which premiered in 1860, is often hailed as Iceland's first successful performed play.