Brown was born in Cloverdale, Tillamook County, Oregon. She attended public schools, the Oregon College of Education at Monmouth, 1922-1924, graduated from the University of Oregon in 1929 with a Bachelor of Arts. She then undertook graduate study at the University of California at Los Angeles from 1936 to 1937. Brown was a teacher in Oregon public schools between 1932 and 1944; in 1937, while teaching in a Portland high school, she met Richard L. Neuberger. The couple married in 1945, after Neuberger completed his service in World War II. Richard Neuberger was subsequently elected to the Oregon State Senate in 1948.

Maurine entered politics herself in 1950 when she was elected a member of the State House of Representatives and served from 1950 to 1955. During this period she was also a member of the board of directors of the American Association for the United Nations. Richard was elected to the United States Senate in 1954. In 1960, Richard died from a cerebral hemorrhage. Maurine then won a special election on 8 November 1960, as the Democratic candidate to fill the vacancy caused by the death of her husband. Hall S. Lusk had been appointed by the governor to the Senate upon Richard's death. After the election, Maurine completed Richard's remaining term from 9 November 1960 to 3 January 1961. At the same time as the special election, she won the general election for the term commencing 3 January 1961 and ending 3 January 1967; she was not a candidate for reelection in 1966. Her activities in government focused on consumer, environmental and health issues, including the sponsorship of one of the first bills to require warning labels on cigarette packaging.

Following her time in the Senate she was employed as a lecturer on consumer affairs and the status of women, and as teacher of American government at Boston University, the Radcliffe Institute of Advanced Studies at Harvard University, and Reed College. She was a resident of Portland, Oregon until her death in 2000.