Born in Chicago, Illinois, Packer grew up in Atlanta, Georgia, and Louisville, Kentucky. "ZZ" was a childhood nickname; her given name is Zuwena. Her writing was published in the magazine Seventeen at the age of 19. Packer is a 1990 graduate of Seneca High School in Louisville, Kentucky.
Packer attended Yale University, receiving her BA in 1994. Her graduate work included an MA at Johns Hopkins University in 1995 and an MFA from the Iowa Writers' Workshop of the University of Iowa in 1999, where she was mentored by James Alan McPherson.
