Skou was educated at the University of Copenhagen. In 1946 he joined the staff of the Institute of Physiology, Aarhus University, where he served as professor of biophysics from 1978 until his retirement in 1988.

Skou has sought to understand how the energy-rich adenosine triphosphate (ATP) molecule fuels cellular activities. It had been established by Peter Mitchell that a greater concentration of ions was normally found on one side of the cell's membrane. How the ions were transported across the membrane, however, remained a mystery. Skou suspected that the process was mediated by an enzyme. In 1957, working with crab nerve cells, Skou found an enzyme in the cell's membranes that appeared to pump sodium out of cells while transporting potassium within, a process since referred to as the Na⁺/K⁺ pump. The enzyme, known as sodium-potassium-ATPase, proved to be the first of many ATP-based enzymes responsible for transporting molecules through cellular membranes.

For his discovery of the Na⁺/K⁺ pump Skou shared the 1997 Nobel Prize for chemistry with Paul Boyer and John Walker.