Some members of a juvenile gang, known as Kishor gang, allegedly hacked a woman entering her house in the city's Rayer Bazaar area.
The incident happened around 9:30 pm on Wednesday.
The injured woman was identified as Sathi Begum, 27, daughter of Nizam Fakir.
She lives in a rented house near Babri Masjid in the area.
Sathi received treatment at Dhaka Medical College Hospital, said Nizam, father of the victim.
He said police on Tuesday arrested some gang members from the area. Other gang members suspected my daughter over the incident and hacked her by entering our house.
Mahfuzul Haque Bhuiyan, officer-in-charge of Mohammadpur Police Station, said they learned about the incident.
Legal action would be taken after receiving a written complaint, he added.