He also said the preliminary test suggested the level of the Ebola virus "was low" in the blood of the nurse, who has been isolated after her symptoms were reported.
And at this time, only one person may have had contact with the nurse after she became sick, Frieden said.
He cautioned that it is possible the US will see additional cases of Ebola in the coming days.
"This is because the health care workers who cared for this individual may have had a breach of the same nature of the individual who appears now to have a preliminary positive test," Frieden added.
Earlier, Texas Health Resources chief clinical officer Dan Varga said in a statement that the nurse's condition is stable and that a close contact has also been proactively placed in isolation.
"We have known that further cases of Ebola are a possibility among those who were in contact with Mr. Duncan before he passed away last week," Varga said.
"The system of monitoring, quarantine and isolation was established to protect those who cared for Mr. Duncan as well as the community at large by identifying any potential Ebola cases as early as possible and getting those individuals into treatment immediately."
Duncan, a 42-year-old Liberian, arrived in Dallas on Sept 20 and fell ill several days later. He had already been showing symptoms during his first visit to Texas Health Presbyterian Hospital on Sept 25. But the hospital did not weigh his case until his second visit on Sept 28.
Duncan was diagnosed to be the first Ebola patient on US soil on Sept 30. He died Wednesday.