Delbrück was born in Berlin, German Empire. His father was Hans Delbrück, a professor of history at the University of Berlin, and his mother was the granddaughter of Justus von Liebig.
Delbrück studied astrophysics, shifting towards theoretical physics, at the University of Göttingen. After receiving his Ph.D. in 1930, he traveled through England, Denmark, and Switzerland. He met Wolfgang Pauli and Niels Bohr, who got him interested in biology.
Delbrück went back to Berlin in 1932 as an assistant to Lise Meitner, who was collaborating with Otto Hahn on the results of irradiating uranium with neutrons. During this period he wrote a few papers, one of which turned out to be an important contribution on the scattering of gamma rays by a Coulomb field due to polarization of the vacuum produced by that field (1933). His conclusion proved to be theoretically sound but inapplicable to the case in point, but 20 years later Hans Bethe confirmed the phenomenon and named it "Delbrück scattering".
In 1937, he moved to the United States to pursue his interests in biology, taking up research in the Biology Division at Caltech on genetics of the fruit fly Drosophila melanogaster. While at Caltech Delbrück became acquainted with bacteria and their viruses (bacteriophage or 'phage'). In 1939, he co-authored a paper called The Growth of Bacteriophage with E.L. Ellis in which they demonstrated that viruses reproduce in "one step", rather than exponentially as cellular organisms do.
In 1941, he married Mary Bruce, with whom he had four children. Delbrück's brother Justus Delbrück, a lawyer, his sister Emmi Bonhoeffer and his brother-in-law Klaus Bonhoeffer (brother of the theologian, Dietrich Bonhoeffer) were in the German Resistance against the Nazi Regime. Klaus and Dietrich Bonhoeffer were executed in the last days of Hitler's Germany.
Delbrück remained in the US during World War II, teaching physics at Vanderbilt University in Nashville while pursuing his genetic research. In 1942, he and Salvador Luria of Indiana University demonstrated that bacterial resistance to virus infection is caused by random mutation and not adaptive change. This research, known as the Luria-Delbrück experiment, was also significant for its use of mathematics to make quantitative predictions for the results to be expected from alternative models. For that work, they were awarded the Nobel Prize in Physiology or Medicine in 1969, sharing it with Alfred Hershey. In the same year together with Salvador Luria he was awarded the Louisa Gross Horwitz Prize from Columbia University.
In 1947, Delbrück returned to Caltech as a professor of biology where he remained until 1977.
From the 1950s on, Delbrück applied biophysical methods to problems in sensory physiology rather than genetics. He also set up the institute for molecular genetics at the University of Cologne.
Delbrück was one of the most influential people in the movement of physical scientists into biology during the 20th century. Delbrück's thinking about the physical basis of life stimulated Erwin Schrödinger to write the highly influential book, What Is Life?. Schrödinger's book was an important influence on Francis Crick, James D. Watson and Maurice Wilkins who won a Nobel prize for the discovery of the DNA double helix. During the 1940s Delbrück developed a course in bacteriophage genetics at the Cold Spring Harbor Laboratory to encourage interest in the field. Delbrück's efforts to promote the "Phage Group" (exploring genetics by way of the viruses that infect bacteria) was important in the early development of molecular biology. On 26-27 August 2007, what would have been his 100th birthday celebration, Cold Spring Harbor Laboratory hosted a meeting of Delbrück's family members and friends to reminisce about the life and work of Delbrück