Born in Syracuse, New York, Monkiewicz moved with his parents to New Britain, Connecticut, in 1899. He attended the public schools and was graduated from New Britain (Connecticut) High School in 1917. He served as an apprentice seaman in the United States Navy (Columbia University Naval Unit), October 3, 1918, to December 17, 1918. He was graduated from the law department of Fordham University, New York City, in 1921. He was admitted to the bar in 1933 and commenced practice in New York and Connecticut. He also engaged in banking. He served as clerk of the New Britain, Connecticut, city and police court from July 1932 to August 1933. He served as prosecuting attorney for the police court from 1937 to 1939.