According to local witnesses, residents heard a loud explosion and saw huge flames billowing from the flower shop on Nguyen Thai Binh street.
Local residents failed in their attempts to put out the fire, which rapidly spread to a jewelry shop nearby.
After the fire alarm was raised, five fire engines and 80 fire fighters rushed to the scene to tackle the blaze.
The fire was brought under control within 15 minutes. The victims were identified as Nguyen Thi Phuong Uyen, aged 15 and Nguyen Thi Van, aged 20.
The owner of the shop, Dinh Thi Hong Nguyet, was absent at the time the fire broke out, however, she did suffer severe burns when trying to save her child from the fire.
The cause of the fire is still being investigated.