Henry Clapp Sherman was born in Ash Grove, Virginia. He attended the Maryland Agricultural College (now the University of Maryland), obtaining a B.S. in 1893 in general science and chemistry. He remained at the school for the next 2 years, pursuing graduate studies until he received a fellowship at Columbia University, where he earned an M.S. in 1896 and a Ph.D. in 1897. From 1898 to 1899 and for several subsequent summers, Sherman served as assistant to W. O. Atwater at Wesleyan University, where working on energy metabolism and nutrition studies. He then joined the faculty of Columbia University, where he spent the remainder of his professional career. He served as lecturer in chemistry (1899), instructor (1901), adjunct professor of analytical chemistry (1905), professor of organic analysis (1907), professor of food chemistry (1911), and Mitchill Professor of Chemistry (1924–1946). He was also chairman of the Chemistry Department from 1919 to 1939.
Sherman's interest in food chemistry had been stimulated by Atwater, a pioneer in the quantitative study of foods and nutrition in the United States. At Columbia Sherman developed a research program to analyze of fats, oils, and food products and soon became internationally known for his precise quantitative studies of vitamins, minerals, and other essential nutrients. In 1910, he turned to the chemistry of enzymes and proteins. He provided experimental evidence that enzymes are essentially pure protein in nature, a finding contrary to the views of many chemists at the time. Between 1910 and 1934 Sherman did research on the properties, activity, and purification of the digestive enzymes, on the efficiency of proteins in the human diet, and on the protein requirements of humans. In 1925 he demonstrated that cysteine is an essential amino acid. Sherman also established the average human requirements for calcium, phosphorus, and iron, and for many years his studies were considered the best guides to the health requirements for these minerals. During the 1920s and 1930s, Sherman's laboratory at Columbia was largely responsible for the quantitative bioassay of many vitamins.
Because of his outstanding work in food chemistry and nutrition, Sherman was asked to serve in many research programs and organizations in the health field. He was an associate of the Carnegie Institution from 1912 to 1929 and from 1933 to 1939. In 1917 he was a member of the American Red Cross mission sent to study the food situation in Russia. He was chief of the Bureau of Human Nutrition of the U.S. Department of Agriculture (1943–1944) and also served as president of the American Institute of Nutrition (1931–1933 and 1939–1940) and of the American Society of Biological Chemists (1925). In 1934 Sherman received the Nichols Medal of the American Chemical Society.