The police have been accused of shooting her with a bean bag round, but the force says it is still not clear what actually happened.
Some have suggested that the injury may have been caused by a projectile thrown or fired by protesters.
Chief superintendent John Tse said they had urged the woman to contact them, but she had not responded.
Meanwhile, the woman has spoken for the first time since she was injured on August 11, condemning what she called police brutality and urging the government to respond to protesters’ demands.
She gave a speech in a video clip which was played at a press conference held by a group of anti-government protesters.
The woman’s right eye was covered with gauze, and she was wearing a pair of sunglasses and a mask.
In the four-minutes of footage – said to have been recorded on August 26 – the woman called on the police “to stop all violent acts”.
She cited the Egyptian mythology of “the eye of Horus”, which is a symbol of protection and good health, saying she hoped her right eye could also “become a beacon of hope that supports Hongkongers, to ward off evil”.
She did not talk about the present state of her injuries during the footage, but thanked people across the world who had showed solidarity with her.