The son of a civil servant, von Laue was born in Pfaffendorf, Koblenz, and educated at the universities of Strasbourg, Göttingen, Munich, and Berlin, where he obtained his doctorate in 1903. He worked in various universities before his appointment as professor of theoretical physics at Berlin University in 1919. He remained there until 1943 when he moved to Göttingen as director of the Max Planck Institute.

Although von Laue began his research career working on relativity theory, his most important work was the discovery of x-ray diffraction in 1912 for which he was awarded the 1914 Nobel Prize for physics. From this discovery much of modern physics was to develop and, some forty years later, the new discipline of molecular biology was to emerge.

Von Laue put together two simple and well known ideas. He knew that x-rays had wavelengths shorter than visible light; he also knew that crystals were regular structures with their atoms probably lined up neatly in rows. Thus, he concluded, if the wavelength of x-rays was similar to the interatomic distance of the atoms in the crystal, then x-rays directed onto a crystal could be diffracted and form a characteristic and decipherable pattern on a photographic plate.

He passed the actual experimental work to two of his students, Walter Friedrich and Paul Kipping, who first tried copper sulfate (1912), which yielded a somewhat unclear pattern. When they changed to zinc sulfide they almost immediately obtained a clear photograph marking out the regular and symmetric arrangement of the atoms in the crystal.