"The level of risk to people around her would be extremely low," said Dr. Tom Frieden, director of the Centers for Disease Control and Prevention.
The worker is the second to be infected after treating a Liberian man who died of Ebola last week.
Frieden says the health care worker travelled to Ohio before she knew that the first nurse had been diagnosed. She was undergoing self-monitoring at the time.
The unidentified nurse flew to Cleveland on Friday, the same day a colleague, nurse Nina Pham, was hospitalized. Pham's diagnosis with Ebola was disclosed on Sunday.
The second nurse returned to Texas on Monday on Frontier Airlines Flight 1143 from Cleveland to Dallas-Fort Worth with 132 other passengers, according to the CDC.
The airplane's crew said she had no symptoms of Ebola during her return flight on Monday. But Tuesday morning she developed a fever and on Tuesday night tested positive for Ebola.
Infected Ebola patients are not considered contagious until they have symptoms. But the CDC is asking passengers on Monday's flight to call the health agency so they can be monitored.
The flight landed in Dallas at 8:16 p.m. Monday, stayed there overnight, and underwent a thorough cleaning before returning to service the next day. The cleaning was consistent with CDC guidelines, according to a Frontier Airlines statement released by CDC officials.
The health worker's flight to Cleveland last week happened far enough in advance of her symptoms that the CDC sees no need to contact passengers on that earlier flight, said Barbara Reynolds, a CDC spokeswoman.
Health officials did not immediately release the reason for her trip or where she visited in the Cleveland area. The CDC notified the airline Wednesday morning.
The CDC is asking passengers on the Monday flight to call 1-800-CDC INFO (1-800-232-4636).