Cvetič earned bachelor's and master's degrees at the University of Ljubljana in 1979 and 1981, respectively. She completed her doctorate at the University of Maryland, College Park in 1984. Her dissertation, Origin of Mass Hierarchies in Gauge Theories, was supervised by Jogesh Pati. After working as a researcher at the Stanford Linear Accelerator Center and the University of Pennsylvania, she joined the University of Pennsylvania faculty in 1989. She became Class of 1965 Endowed Term Professor in 1999, and Fay R. and Eugene L. Langberg Endowed Chair in 2003.