His first business was selling dance lessons by mail, using a kinetoscope. Though the idea was successful, he had problems with the business, which failed. His second business was drawing and selling "footprints", (an unusual use of drafting skills) which prospective dancers could place on the floor and follow to learn how to dance. This mail-order business remained successful. His third business, launched in 1925, involved selling branded dance lessons through franchising. He trained dance instructors for the Statler Hotel chain, who then went to various hotels and gave lessons, Murray kept some of the profits from each franchise. This business was expanded more widely in 1938, when an Arthur Murray dance studio franchise was opened in Minneapolis, Minnesota, others followed. At one time, there were over 3560 dance studios bearing his name as of 1964, but by 2003 there were only about 180 studios. Arthur Murray Dance Studios claims to be the second oldest franchised company (A&W Restaurants began in 1919).
Murray went on television with a dance program, hosted by his wife Kathryn Murray, running from 1950 - 1960, first on CBS, then ABC, and then back to CBS. The Murrays retired in 1964.
Pupils of Murray include: Eleanor Roosevelt, the Duke of Windsor, John D. Rockefeller Jr, Cornelius Vanderbilt Whitney, Barbara Hutton, Elizabeth Arden and Jack Dempsey.
The Murrays had twin daughters.