Ejnar Møbius’ father came from Saxony to Denmark shortly before Ejnar was born. He represented the Aarhus Gymnastikforening and competed in the individual all-around in gymnastics at the 1912 Olympic Games in Stockholm. In the same year, he won the Danish Championships in individual gymnastics. Like his father and at least one brother, he worked for the Danish State Railways. In 1916, Ejnar became a train driver’s assistant in 1916 and was promoted to train driver in 1930. He worked in Korsør on the island of Seeland. In 1916, he married Gudrun Elisabeth Marie Friis. They had two sons.