The son of a distinguished educationist, von Kármán studied engineering at the Polytechnic in his native city of Budapest. After graduating in 1902 he taught at the Polytechnic until 1906 when he moved to Göttingen, where he completed his PhD in 1908. At about this time his interest in aeronautics was aroused when he saw Henri Farman fly a biplane in Paris. He pursued his new interests further at Göttingen when he was asked to help Ludwig Prandtl design a wind tunnel for research on airships. Von Kármán continued to work in aeronautics and in 1912 he was invited to establish and direct a new institute of aerodynamics at the University of Aachen. Here he remained until 1930, apart from the war years spent in Austria working at the Military Aircraft Factory, Fischamend. In 1930, unhappy with political conditions in Germany, he moved to the California Institute of Technology to set up and direct another new institute, the Guggenheim Aeronautic Laboratory at Pasadena, California. He became a naturalized American in 1936.

Von Kármán remained director of the Guggenheim Laboratory until 1949. During this time he contributed to many branches of aeronautics and encouraged work on jet propulsion, rockets, and supersonic flight. At von Kármán's insistence the world-famous Jet Propulsion Laboratory was set up in 1938 and he served as its director until 1945. He also served as a consultant to the US Army Air Corps from 1939 onward. After his retirement from Pasadena he organized the Advisory Group for Aeronautical Research and Development to provide NATO with technical advice.

Among his many contributions to aerodynamics, von Kármán is probably best known for his discovery in 1911 of what have since been called Kármán vortices – the alternating vortices found behind obstacles placed in moving fluids. The basic idea was drawn to his attention by a graduate student in Prandtl's laboratory. He had been asked to measure the pressure distribution around a cylinder placed in a steady flow. But, the student found, the flow refused to move steadily and invariably oscillated violently. Prandtl insisted the fault lay with the student who had not bothered to machine circular cylinders. Von Kármán would enquire of the student daily how the flow was behaving and was daily given the sad reply that the flow still oscillated. Eventually von Kármán came to see that the student had stumbled upon a genuine effect. Over a weekend he calculated that the wake should indeed separate into two periodic vortices. Further, there is a symmetric arrangement of vortices which is unstable; only an asymmetric arrangement of vortices persists when the conditions are changed.

Von Kármán went on to demonstrate that above a certain velocity v, where d is the cylinder's diameter, vibrations will be induced with a frequency v/d cycles per second. It was precisely these vibrations which were induced in 1940 in the Tacoma Narrows suspension bridge when v exceeded its critical velocity of 42 mph.