Carl Holm took up junior football at the age of 12 and spent his entire domestic senior career, from 1946 through 1958, with Boldklubben 1903. Internationally, he made three appearances with the Danish national team between 1949 and 1952, two of which occurred in the latter year, and was selected to represent his country at the 1952 Helsinki Games. Although Denmark won its first two matches, defeating Greece and then Poland before being eliminated in the quarter-finals by upcoming silver medalist Yugoslavia, Holm remained a reserve and did not play at the Games. He retired from active competition after 1958 and settled into private life.