Görgl is the daughter of Traudl Hecher (b. 1943), an alpine racer for Austria in the early 1960s. She won Olympic bronze medals in the downhill in 1960 (at age 16) and 1964, and remains the youngest Olympic medalist in alpine skiing. Görgl's older brother Stephan (b. 1978) is a former World Cup alpine racer; he competed in the giant slalom at the 2006 Winter Olympics.