Svensson was born and raised in Höllviken, south of Malmö. She was regarded as one of the best and most promising young Swedish boxers thanks to her successful amateur career, during which she won a medal in every World Championship event in which she participated. At the 2006 World Championships she won a silver medal, which was followed by bronze at both the 2008 and 2010 events. She also won bronze and silver at the 2006 and 2007 European Championships, respectively.