Felser studied chemistry and physics at the University of Cologne, completing there both her diploma in solid state chemistry (1989) and her doctorate in physical chemistry (1994). After postdoctoral fellowships at the Max Planck Institute for Solid State Research in Stuttgart, Germany (1994-1995) with Arndt Simon and Ole Krogh Andersen, she moved to the Centre National de la Recherche Scientifique (CNRS) in Nantes, France (1995-1996), where she worked in the group of Jean Rouxel. Afterwards, she joined the Johannes Gutenberg University of Mainz in 1996 as an assistant professor (C1). She resided there in 2002 and was appointed to a full professor (C4) in 2003.
In 1999, she was a visiting professor at Princeton University and, in 2000, at the University of Caen. From 2009 to 2010 she was visiting professor at Stanford University and in 2019 visiting professor at Harvard University in the department Physics/ Applied Physics.
Since September 2011 she is a director of the Max Planck Institute for Chemical Physics of Solids and Professor hon. at the TU Dresden. Since June 2023, Felser has been Vice President of the Max Planck Society (CPT section).