Petersen was born at Saltnes in Eysturoy. He was the son of Johannes Petersen (1812–1901) and Susanne Frederikke Olesdatter (1826–1905). He became a student in Reykjavik, Iceland in 1875 and was awarded his Cand.theol. in 1880. He was ordained a Lutheran priest in the Church of the Faroe Islands (Fólkakirkjan). He served as parish priest at Sandoynni (1880), Suðuroy (1885) and at Østerø (1900). He was a rural dean at Nes in Eysturoy from 1900 to 1917. 
Petersen was chairman of the Sambandpartiet from its foundation in 1906 until his death in 1917. He was a member of the Faroese Løgting (1890) and the Danish Landsting (1892–1900). He served as county councilor for the Faroe Islands 1894–1902. 
Frederik's Church in NesEdit
Fredericks Church (Fríðrikskirkjan) in Nes was completed in 1994 and was named in honor of Fríðrikur Petersen.