Šašić began her career at the age of five at TuS Germania Hersel, after her older brother had taken her to a training session.

After several clubs at junior level, Šašić joined the Bundesliga side SC 07 Bad Neuenahr in 2004.

In 2005, Šašić received the Fritz Walter medal in bronze as the year's third best female junior player.

[5] In March 2007, she suffered a fractured tibia in a league game against Bayern Munich, which ended her season.

Later that year, she was part of Germany's winning squad at the 2004 FIFA U-19 Women's World Championship, scoring three goals in the group stage.

She was part of Germany's squads claiming bronze at the 2008 Summer Olympics and winning the title at the 2009 European Championship, where she scored in the semi-final against Norway.

However, she went on to miss a vital penalty kick versus the United States in the semifinals as Germany was eliminated.