Munch grew up at Gjerpen parsonage, where his father was parish priest of the Church of Norway. He was schooled in the city of Skien. He attended the Royal Frederick University. Munch first studied law and took his state examination in 1834, but then turned to historical and philological studies.
Munch's first great achievement, with Rudolph Keyser, was their three volumes of Norges Gamle Love (Norway's old laws), edited after a two-year research visit to Copenhagen. In 1837, he became lecturer in history at the University of Oslo and in 1841 became a professor of history. In 1857, after producing numerous publications, he received a large grant for archives research in Rome and lived there from 1859 to 1861. Munch served as Norway's national archivist from 1861 to 1863. He was one of the first non-Catholics to be allowed into the archives of the Vatican. He took extensive notes from the volumes of papal letters, and sometimes drew accurate facsimiles of the texts. His research there was useful in his main work, Det norske Folks Historie (History of the Norwegian People), in eight volumes, and he sent his notes home to the Royal Archives in Christiania. Among the theories he is remembered for is the theory on immigration to Norway, in which he developed work done by Rudolf Keyser. On a trip back to Rome to fetch his family, who had remained there for a while, he died from a stroke, and was buried in the Protestant cemetery in Rome.
In this work, Munch translated the 3rd Chronicle from a Codex transferred to the British Museum (formerly owned in 1620 by one Sir Robert Cotton). The manuscript is the only known copy of this Codex (and thought to be the only one). In any event, Munch translated runic characters and added historical notes to lend light upon the writings, and using previous works on the history of Scottish and Icelandic Isles to aid in the presentation of the translated material.
Peter Munch had racial thoughts on certain peoples, e.g. Finns and Hungarians. He despised Finns and claimed that they cannot have an independent country because of their low state of civilization, as he claimed. Peter Munch claimed in his article on Finnish nationality (Om Finlands Nationalitet og dens Forhold til den svenske) in 1855, that Finns and Hungarians must have a human race of their own.