Brown was born in St. Ignace, Michigan and attended the public schools there. He attended the University of Illinois at Urbana-Champaign and graduated from Albion College in Albion, Michigan in 1911. He studied law and was admitted to the bar in 1914 and commenced practice in St. Ignace. He was prosecuting attorney of Mackinac County 1914-1926 and the city attorney of St. Ignace 1916-1928. He was an unsuccessful candidate for election in 1924 to the United States House of Representatives and in 1928 for election as justice of the Michigan Supreme Court. He was a member of the State Board of Law Examiners 1930-1942.

Brown was elected as a Democrat to the United States House of Representatives for the Seventy-third Congress and was reelected to the Seventy-fourth Congress, serving from March 4, 1933, until his resignation, effective November 18, 1936. He was elected as a Democrat on November 3, 1936, to the United States Senate for the term beginning January 3, 1937, but was subsequently appointed to the United States Senate to fill the vacancy caused by the death of James Couzens for the term ending January 3, 1937. In total, he served from November 19, 1936, to January 3, 1943. He was an unsuccessful candidate for re-election in 1942. He was chairman of the U.S. Senate Committee on Claims in the Seventy-seventh Congress. He was an administrator in the Office of Price Administration in 1943 and resumed the practice of law in both Washington, D.C., and Detroit, Michigan. He also served as chairman of the Detroit Edison Company. He was chairman of the Mackinac Bridge Authority until his death in St. Ignace. He is interred in Lakeside Cemetery there.

In 2004, Albion College renamed its Honors Institute the Prentiss M. Brown Honors Institute in memory of the 1911 alumni.