Police in Sahiwal District, in Pakistan's eastern Punjab province, said most of the incidents happened after sunset, but some of the younger victims were also attacked while returning home after school.
Most of the women in the town of Chichawatni, which is 300 miles south of the capital, were stabbed on the legs, stomach or back. Some required stitches or surgery
The attacker's motives are unclear, although police said he may be insane.
Dr Asim Waqar at Chichawatni hospital said: "Two of the women were wearing a burqa at the time they were attacked."
In the most recent attack, a man on a motorbike dismounted and stabbed a 22-year-old multiple times as she was standing outside her house with her sister.
The police are hunting a single attacker and have offered a £1500 reward for his arrest.
Many victims who sought treatment have not reported the attacks because the police have a poor reputation and they are forbidden by tradition to speak to strange men.
Violence against women is common in Pakistan and activists say several are murdered each day.
Underfunded police rarely solve the cases, which can take years to work their way through congested courts.