Meusburger grew up in Heidelberg, where she graduated from Kurfürst-Friedrich-Gymnasium. She then went on to study physics at the University of Freiburg from 1996 to 2001, where she wrote the thesis The Quantisation of the algebra of invariants of the closed bosonic Nambu–Goto String using a concrete realization, for which she won the Gustav-Mies Prize 2002 for best thesis, and graduated with distinction. Two months later she was at the Heriot-Watt University in Edinburgh to work on her PhD in the department of mathematics under supervision of Bernd Schroers ; her thesis was titled Phase space and quantisation of (2+1)-dimensional gravity in the Chern–Simons formulation. Between 2004 and 2008, she worked as a postdoc at the Perimeter Institute in Canada. After a half-year stay at the University of Nottingham as a Marie Curie Intra European Research Fellow, she led a Emmy-Noether Junior Research Group at the University of Hamburg until 2011.