Fischer, who has been head of media for over three years, has also handled FIFA's World Cup communications since 2007, and had served in a variety of marketing and communications roles at the governing body before that.
"As a passionate football fan, I feel privileged to have contributed to the growth and betterment of the game as part of FIFA's organisation for more than a decade," Fischer said.
Commenting on her decision to step aside, FIFA's chief comms officer Fabrice Jouhaud said: "We respect her decision to leave and wish her the very best in her future professional career."
The search for Fischer's replacement is ongoing, a FIFA spokesman told PRWeek.
FIFA has been plagued with controversy recently, culminating in the banning of then president Sepp Blatter in 2015. Prior to the ban, Blatter had served as FIFA president for 17 years and had spent over 40 years at the governing body.
He was removed from his post for approving a payment of over £1.3m to Frenchman Michel Platini in 2011, who was also banned by FIFA.