Williams was born in New York City to Marsha Garces Williams, the second wife of Robin Williams. The first of Marsha's two children, Zelda has an older half-brother from Robin's first marriage, Zachary Pym Williams (born April 11, 1983), as well as a younger brother Cody Alan Williams (born November 25, 1991). Williams was named after Princess Zelda, a fictional character in the "Legend of Zelda" video game series, due to Robin Williams's love of the series. Zelda moved to Los Angeles from her hometown of San Francisco.

Williams has been quoted as saying she's played "every single sport on the face of the planet." She regularly visits an indoor climbing gym in her hometown of San Francisco. Williams is also a dedicated video game player and Halo 3 fan and stated that Wikipedia is one of the websites she visits frequently.

Williams's acting debut was in the 2004 film House of D opposite Anton Yelchin as his young first love, Melissa Loggia. In House of D, she worked alongside her father, co-star Robin Williams. Though the film received mixed reviews, Zelda's and Yelchin's performances were well received. In 2007 she was in the independent film Were the World Mine, and has recently wrapped shooting the horror films Don't Look Up and Detention, and the thriller Luster in Los Angeles. In February 2010 she was reported to be cast in the lead role of the thriller Powder Burns, in which she would portray Emily Tomassini, an intelligent, devoutly religious sociopath.