Born Suzana Drobnjakovic to a Serb father and Italian mother, Alexander began acting in school productions at the seventh grade. She was also an ice skater, but had to stop due to an injury. She continued acting through high school and college, and then moved to New York to act in summer stock and Shakespeare festivals. She graduated from the University of Southern California's School of Cinema-Television.

Alexander was a regular on two short-lived series, the medical drama Presidio Med and ABC's twenty-something drama Wasteland. She appeared on the fourth season of Dawson's Creek as Gretchen Witter, dating the title character, and in an episode of the short-lived Fox comedy series Greg the Bunny, playing the part of a lesbian TV Guide reporter and shared a memorable onscreen kiss with Sarah Silverman. Alexander has also appeared in the films Lucky 13, All Over the Guy, and Twin Falls, Idaho. Her role on NCIS ended in May 2005.

Alexander is engaged to director Edoardo Ponti and they are expecting a child in 2006.