Klein won the silver medal in the middleweight class in the 1912 Summer Olympics. This was the first Olympic medal won by Estonia. In the semifinal against Finnish wrestler Alfred Asikainen (both Finland and Estonia were under Russian domination, but Finland, unlike Estonia, was allowed to compete under their own flag), the two grappled for 11 hours and 40 minutes until finally Klein managed to pin Asikainen. Klein was so exhausted from the bout - the longest wrestling match ever recorded - that he was unable to wrestle for the gold the next day, leaving Swedish wrestler Claes Johansson with the gold medal.
The international Martin Klein Memorial in Greco-Roman wrestling is held in Viljandi, Estonia from 1962.