Monahan was born in Swan Hill, Victoria, to Mary Frances (née Nolan) and Patrick Martin Monahan. He attended St Patrick's College, Ballarat, before going on to study law at the University of Melbourne. Monahan was admitted to the bar in 1923, and opened his own chambers in 1931. He developed a reputation as one of Melbourne's leading personal injury and criminal defence lawyers. Monahan appeared in over 100 murder trials, and only one of his clients was ever executed. He was appointed King's Counsel in 1947.
In March 1955, Monahan was appointed to the Supreme Court of Victoria in an acting capacity. His appointment was confirmed in October 1955. On the court, Monahan mainly adjudicated criminal trials, personal injury matters, and divorce cases. He was created a Knight Bachelor in 1967, and retired in 1970, succeeded by Ninian Stephen. Outside of his work, his chief passion was horse racing – he once won £50,000 betting on the Irish Derby. Monahan married Lillie Elevia Bowman in 1929; they had four children.
- Charles Francis, 'Monahan, Sir Robert Vincent (1898–1975)', Australian Dictionary of Biography, National Centre of Biography, Australian National University, http://adb.anu.edu.au/biography/monahan-sir-robert-vincent-11146/text19853, published first in hardcopy 2000