Born in Tehran to an Armenian-Persian family, Alfred Ter-Mkrtchyan took up wrestling in 1986. After winning the 1990 European junior title, Ter-Mkrtchyan, who competed in the Greco-Roman flyweight class for the most of his career, was selected for the Soviet national team in 1991. Representing the Soviet Union, Ter-Mkrtchyan won bronze at the 1991 European Championships, which he improved to gold in 1992. Later that year, representing the Unified Team, Ter-Mkrtchyan won silver at the 1992 Olympics. After the Games, Ter-Mkrtchyan moved to the United States with his family and later to Germany, becoming a naturalized German citizen in November 1993, and represented his new country from that time. In September 1993 Ter-Mkrtchyan competed under the German flag for the first time and won bronze at the World Championships. He was World Champion in 1994 and won three more bronze medals at the World Championships (1995, 1997, 1999). He also won silver at the 1995 European Championships and bronze at the 1994, 1996 and 2000 European Championships. Ter-Mkrtchyan retired from sports after not making the German 2004 Olympic team.