Alexander was born Suzana S. Drobnjaković (Serbian Cyrillic: Сузана С. Дробњаковић) in Los Angeles, California, to Serbian parents. She began acting in school productions in the seventh grade. She also was an ice skater but had to stop due to an injury to her knee. She continued acting through high school and college, and then moved to New York to act in summer stock and Shakespearefestivals. She graduated from the University of Southern California's School of Cinema-Television before going on to have a successful acting career in both TV and film.