The worker at the Texas Health Presbyterian Hospital had been wearing protective gear during treatment of the patient Thomas Eric Duncan, who died last week. The worker reported a low-grade fever on Friday night and was isolated and referred for testing, health officials said on Sunday.
"We knew a second case could be a reality, and we've been preparing for this possibility," said Dr. David Lakey, commissioner of the health service.
The worker is the first person in the United States to test positive for Ebola who has not been to West Africa, where an outbreak has killed more than 4,000 people, mostly in Liberia, Sierra Leone and Guinea.
Texas officials did not identify the health worker or give any details about the person, but CNN said it was a woman nurse.
New York's John F. Kennedy Airport on Saturday began the screening of travelers from the three hardest hit West African countries. Liberia is the country worst affected by the virus with 2,316 victims, followed by 930 in Sierra Leone, 778 in Guinea, eight in Nigeria and one in the United States, the World Health Organization said on Friday.
Some 4,033 people are known to have died in seven countries from the outbreak, it said. Ebola is spread through contact with bodily fluids of an affected person or contamination from objects such as needles.
People are not contagious before symptoms such as fever develop. The United Nations said on Friday that its appeal for $1billion to respond to the West Africa outbreak was only 25 percent funded.
In Europe an assistant nurse infected with the Ebola virus is showing signs of "slight improvement", the Spanish government said on Sunday,But a statement released by Spain's government said Romero's prognosis remains serious and further complications cannot be ruled out.
Another Spanish nurse, who had also treated a patient infected with the virus in Africa, was released from Madrid's Carlos III hospital on Saturday after twice testing negative for Ebola.
That patient, Manuel Garcia Viejo, died of Ebola on September 25. He had been medical director of a Sierra Leone hospital for 12 years.
Fifteen other people, mostly hospital staff as well as Romero's husband, are under observation at the Carlos III hospital where Romero is being treated. The hospital said none of them were showing any symptoms.
The latest case in US underlines United Nations fears and growing concerns in the United States about Ebola, for which there is no vaccine or widely available treatment.
"The virus is far ahead of us and every day the situation gets worse," the head of the United Nations' emergency Ebola mission, Anthony Banbury, told UN leaders after a tour of Liberia, Guinea and Sierra Leone, the nations hardest hit by the epidemic.
The CDC has predicted the number of cases globally could mount in a worst-case scenario to 1.4 million by January, unless strong measures are taken to contain the disease.
The WHO reported 4,033 people have died from Ebola as of October 8 out of a total of 8,399 registered cases in seven countries.The sharp rise in deaths came as the UN said aid pledges to fight the epidemic have fallen well short of the $1 billion (800 million euros) needed.
IMF chief Christine Lagarde pleaded on Saturday for the world to remember that not all of Africa had been hit with Ebola.With Sierra Leone, Guinea and Liberia already seeing their economies crumble because of the disease, Lagarde emphasized: "We should be very careful not to terrify the planet in respect of the whole of Africa."