Born in New York City, Muller was awarded a scholarship to Columbia University in 1907 and specialized in heredity during his undergraduate studies. On graduation he took up a teaching fellowship in physiology at Cornell Medical School, gaining his master's degree in 1912 for research on the transmission of nerve impulses. During this period he continued working at Columbia in his spare time, contributing to the genetic researches on Drosophila fruit flies. He was employed officially at Columbia in 1912 and received his PhD in 1916 for his now classic studies on the crossing over of chromosomes. He was also a coauthor of The Mechanism of Mendelian Heredity (1915), a fundamental contribution to classical genetics.

In 1915, at the request of Julian Huxley, Muller moved to the Rice Institute, Houston, Texas, where he began studying mutation. By 1918 he had found evidence that raising the temperature increases mutation rate. In 1920, after a brief spell back at Columbia, he joined the University of Texas as an associate professor, becoming a professor in 1925. In 1926 he found that x-rays induce mutations, a discovery for which he eventually received the 1946 Nobel Prize for physiology or medicine.

In 1933 Muller spent the first of eight years in Europe at the Institute for Brain Research, Berlin. Hitler's rise to power forced him to leave Germany and he moved to the Academy of Sciences, Leningrad, at the invitation of Nikolai Vavilov. Muller believed that in a communist state he would be able to develop his own socialist ideas and apply his research to improve the human condition. However, the advent of Lysenkoism effectively hampered most genetic research in Russia and Muller left, volunteering to serve in the Spanish Civil War. He then worked at the Institute of Animal Genetics, Edinburgh, returning to America in 1940. He held a position at Amherst College, Massachusetts, from 1942 until 1945, when he became professor of zoology at Indiana University, remaining there for the rest of his life.

Muller made important theoretical contributions to genetics. He visualized the gene as the origin of life, because only genes can replicate themselves, and he believed all selection and therefore evolution acted at the level of the gene. He worried about the increasing number of mutations accumulating in human populations, which can survive because of modern medical technology, and proposed a program of eugenics to overcome the problem. He fully realized the harm to human chromosomes that can result from ionizing radiation and campaigned against excessive use of x-rays in medicine, careless handling of nuclear fuels, and testing of atomic bombs.

Muller is seen by many as the most influential geneticist of the 20th century, mainly through his appreciation of genetic mutation as fundamental to future genetic research. He published over 350 works, the most important paper being Artificial Transmutation of the Gene (1927).