Grant is the only daughter of actors Cary Grant and Dyan Cannon. Her parents divorced when she was two years old, but she had a close relationship with her father for the rest of his life. Partly because her father did not want her to become an actress, she tried other things for several years. After graduating from Stanford University in 1987 with a degree in history and political science, she worked for a law firm, and followed that with a job as a chef. In 1993, seven years after Cary Grant's death, she played her first acting role in the Aaron Spelling television drama Beverly Hills, 90210, in the recurring role of Celeste Lundy. She appeared as a guest star in a variety of shows including Friends, and later appeared in several movies.
She was married to Randy Zisk for three years, but the marriage ended in divorce in 1996. Grant has volunteered as an actress and mentor with the Young Storytellers Program. On August 12, 2008, Jennifer gave birth to a son, Cary Benjamin.