Klein was born to a farmer and started training in wrestling only in his twenties. He left home aged 17 to work as a sailor, but after two years, together with his brother, signed up to a factory in Saint Petersburg, which was then the capital of the Russian Empire. Seeking additional incomes, he became a night-shift guardian in a wrestling club and in this way was introduced to the sport.^[4]

In 1910 Klein won his first title, at St. Petersburg Championships in the unlimited class. Besides the 1912 Olympics, he also competed at the 1913 World Championships, but withdrew due to a hand injury. The same year he won the Russian heavyweight title. During World War I he served in the Russian army and later took part in the Estonian War of Independence. In 1919 he became a wrestling coach and prepared Estonian wrestlers for the 1920 Olympics. At those Games he was also offered a place as a competitor, but refused in favor of his younger teammates. Klein continued coaching and competing in wrestling in Estonia until 1937. He died as a consequence of a hernia, which he developed when moving logs and was buried in the Tarvastu cemetery. Since 1962 an international Martin Klein Memorial in Greco-Roman wrestling is held in Viljandi, Estonia.^[4]