Nguyen Thi Hanh, 29, was found dead at the Thai Binh Lung Hospital early last month.
Her family refused an autopsy, saying she had died of a stroke.
Following further investigations, on December 27 the police arrested Lai Thi Kieu Trang, 25, on suspicion of murdering Hanh.
Trang wanted to kill her cousin, who also works at the hospital, over relationship disputes, the police said. On December 2 she bought six cups of bubble tea, poured cyanide into four of them, and had them delivered to the hospital as thank-you gifts from patients. Bubble tea is a popular drink in Vietnam, especially among young people.
Since Trang's cousin was not present at the time, Hanh took the tea and put it in a fridge. The next morning she drank one of the poisoned cups and died instantly. Two of her colleagues drank two cups that were not poisoned and were safe.
The police exhumed Hanh's remains to do an autopsy on Tuesday to confirm the cause of death.
Further details of the invesigation have not been revealed.
Exposure to certain forms of cyanide at certain concentrations could be fatal within minutes, according to the World Health Organization.