The man, a resident of the neighboring Bac Giang Province, has admitted to killing her, the police said without disclosing his identity.
They are looking into all relevant evidence and his testimony to expand their investigation, they added.
The victim, identified only as Linh, 20, was from the north-central province of Thanh Hoa and had moved to Hanoi to work after dropping out of high school.
After a few years she had become the manager of several apartments in the capital. Owners would hire her to manage their properties and liaise with tenants.
Linh returned from her hometown after the Tet holidays and told her family on Feb. 16 that she had to meet a prospective tenant and show an apartment that day.
Her family could not contact her through the day and even that night.
The last time Linh was seen alive was at 6:35 p.m. on an apartment building security camera in Thanh Xuan District.
On Monday afternoon her body was found at a seven-floor condo in an alley off Cau Giay Street at the intersection of Cau Giay and Thanh Xuan Districts.