Nshan started boxing in Armenia in 1976. He began boxing under the Soviet Union. Munchyan won a gold medal at the 1987 European Amateur Boxing Championships. After the Union's fall in 1991, Munchyan began representing his native Armenia. He won a gold medal at the 1993 World Amateur Boxing Championships and a gold medal at the 1994 World Cup. He is the first boxer from the independent Republic of Armenia to win a medal in either competition.