The Cary store will be at the northeast corner of High House and Davis in the Bradford Shopping Center.
Publix said the opening date will depend on several factors, including permitting and completion of the store's construction; however, the opening is tentatively planned for late 2014.
"We've made a commitment to North Carolina and its residents to bring our level of stellar service and quality products to market in order to provide customers with the superior shopping experience they deserve," said Maria Brous, Publix media and community relations director.
The Florida-based chain has gradually been increasing its presence in the Southeast. It already has stores in the greater Charlotte area.
Publix is one of the most profitable grocery chains in the country and features an employee-owned business model.
"As company owners, we are passionately focused on our customers. We believe that if we take care of our associates, they in turn will take care of our customers, and together we will make our communities a better place. This is our culture, and we are excited about sharing it with North Carolina just as we have in the other five states in which we operate," said Brous.
Publix said it continues to aggressively look for additional locations throughout the state.