Planck was born in Kiel, Holstein, to Johann Julius Wilhelm Planck and his second wife, Emma Patzig.

In 1867 the family moved to Munich, and Planck enrolled in the Maximilians gymnasium school, where he came under the tutelage of Hermann Müller, a mathematician who took an interest in the youth, and taught him astronomy and mechanics as well as mathematics. It was from Müller that Planck first learned the principle of conservation of energy. Planck graduated early, at age 17. This is how Planck first came in contact with the field of physics.

After studying at the University of Munich, he went to the Friedrich Wilhelms University in Berlin for a year of study with physicists Hermann von Helmholtz and Gustav Kirchhoff and mathematician Karl Weierstrass, and in October 1878 Planck passed his qualifying exams .

In April 1885 the University of Kiel appointed Planck as associate professor of theoretical physics. Further work on entropy and its treatment, especially as applied in physical chemistry.

In March 1887 Planck married Marie Merck (1861–1909), sister of a school fellow, and moved with her into a sublet apartment in Kiel.

In 1889 he was named the successor to Kirchhoff's position at the Friedrich-Wilhelms-Universität in Berlin presumably thanks to Helmholtz's intercession – and by 1892 became a full professor.

He published his Treatise on Thermodynamics in 1897. He proposed a thermodynamic basis for Svante Arrhenius's theory of electrolytic dissociation.

After several happy years, in July 1909 Marie Planck died, possibly from tuberculosis.

In March 1911 Planck married his second wife, Marga von Hoesslin (1882–1948).

The discovery of Planck's constant enabled him to define a new universal set of physical units (such as the Planck length and the Planck mass), all based on fundamental physical constants upon which much of quantum theory is based. In recognition of Planck's fundamental contribution to a new branch of physics, he was awarded the Nobel Prize in Physics for 1918 (he actually received the award in 1919).

He retired from Berlin on 10 January 1926, and was succeeded by Erwin Schrödinger.

In February 1944 his home in Berlin was completely destroyed by an air raid, annihilating all his scientific records and correspondence.

In 1944, Planck's son Erwin was arrested by the Gestapo following the attempted assassination of Hitler in the 20 July plot. He was tried and sentenced to death by the People's Court in October 1944. Erwin was hanged at Berlin's Plötzensee Prison in January 1945. The death of his son destroyed much of Planck's will to live.

After the end of the war Planck, his second wife, and his son by her were brought to a relative in Göttingen, where Planck died on October 4, 1947.