The tourist, transferred to Police Hospital No. 199 at 9 a.m. Monday from Son Tra District Health Center with signs of coughing and fever, was suspected of Covid-19 infection.
However, during a pre-quarantine health check, she managed to flee, with the city's epidemic prevention and control team as well as police in Son Tra District in hot pursuit.
"At around 9:30 a.m., police in Phuoc My Ward in Son Tra District announced they had found her. We will move her back to quarantine," Dr Truong Xuan Hung from Police Hospital No. 199 said.
Smith entered Vietnam on February 13. She traveled to mainland China and Taiwan before arriving in Da Nang, where there are six confirmed cases of Covid-19.
As of Monday, 110 people suspected of contracting the virus in the city are being monitored in hospitals, including four foreigners.
In all, Vietnam has had 194 confirmed cases, including 55 who have been discharged from hospital.
Many of the active cases are people coming from Europe or the U.S. and people who had close contact with them.
The government decided Sunday to suspend all international flights to Vietnam and limit flights from Hanoi and Ho Chi Minh City to other provinces and vice versa in the coming two weeks.
Starting March 22, Vietnam also suspended entry for all foreign nationals, including those of Vietnamese origin and family members with visa waivers.
To date, the Covid-19 pandemic has killed more than 34,000 people after spreading to 199 countries and territories.