The woman were in direct contact with two British nationals at the Dien May Xanh supermarket in the central city of Da Nang on March 4.
The two British nationals arrived in Viet Nam from the UK on March 2 and they are among 10 British passengers tested positive for the virus.
The latest patient is being quarantined and treated at a clinic in Da Nang city, according to the Ministry of Health.
As of Wednesday morning, Viet Nam has reported 35 infection cases, of whom 16 had been cleared of the virus and exited hospitals.
At least 2,555 people have been tested negative for the virus and 113 suspected cases have been quarantined.
Nguyen Hong Nhung, 26-year old woman from Ha Noi, returning home from the UK on March 2.
- A 27-year old man, native of Thai Binh, returning home from South Korea on March 4.
- Two patients having been in close contact with Nhung
- A 61-year old man who was on the same flight VN005 with Nhung
- Eleven foreign nationals, including 10 British citizens and one from Ireland.
- A 24-year old woman who met Nhung on February 27 in London, the UK
- A 51-year old woman returning home from the US on March 2.
- A 29-year old woman having been in direct contact with two British patients./.