Kreutzberg was born at Reichenberg/Liberec. Trained at the DresdenBallet School, he also studied dance with Mary Wigman and Rudolf Laban. Beginning in 1927 he appeared in plays directed by Max Reinhardt and in 1929 went with Reinhardt to New York City. Kreutzberg then toured the U.S., Canada, and Europe with the dancer Yvonne Georgi.
An important figure of the German modern dance, he founded a school in Bern in 1955. Its ballets combined the drama and humor, with an emphasis on inventive scenes. He died in Bern.
Kreutzberg made a rare appearance on television in the 1960s, when he was featured in the dual roles of Drosselmeyer and the Snow King, in a heavily abridged German-American co-production of Tchaikovsky's The Nutcracker. It was shown in the U.S. in 1965 by CBS, and repeated several times afterward, but eventually superseded by the nearly full-length Baryshnikov version in 1977.
In 1932–1936, Kreutzberg, along with his partner Ruth Page, created a new and unlikely partnership. Kreutzberg was a German modern dancer, while Page was an Americanballerina. They first performed together on 25 February 1933 in Chicago. This partnership helped Kreutzberg perform his solo acts in other venues, which is what people really enjoyed watching him do. Kreutzberg’s performances were described as including everything from strong actions to flowing movements and even some pantomime. His jumps were very energetic and strong, but yet his body movements were very soft and fluttery. He was known as not just a talented ballet and modern dancer, but as an entertainer.