The shooting was reported just after midnight at the Benning Market in the 2000 block of Benning Road in the northeast.
She was taken to the hospital with non-life-threatening injuries.
No one else inside the store was injured.
Investigators are looking for a man in his 40s, wearing a black hooded sweatshirt, black pants, black shoes, and armed with a silver handgun.
He was last seen heading westbound on Benning Road riding a green bicycle.