"We continue to be incredibly appreciative of the kindness and compassion shown to David and our entire family during this difficult time," the statement read.
Ortiz was shot in the Dominican Republic on June 9, resulting in a 9 mm bullet passed through his intestines and internal organs.
He underwent emergency surgery in the country before being airlifted to Boston the following day.
On June 22, he was moved out of intensive care following a second surgery at Massachusetts General Hospital.
Eleven suspects have been arrested and charged in the shooting.