The female health worker infected is in an isolation ward in stable condition, awaiting confirmation of her diagnosis.
Tom Frieden said a full inquiry would be made into how the transmission occurred.
He said 48 other people who may also have had contact were being observed.
The health worker at Texas Health Presbyterian Hospital wore full protective gear while treating Ebola victim Thomas Eric Duncan, health officials in Dallas say.
Thomas Eric Duncan, who caught the virus in his native Liberia, died on October 8.
The current Ebola outbreak, concentrated in Liberia, Guinea and Sierra Leone, has resulted in more than 8,300 confirmed and suspected cases, and at least 4,033 deaths.
Dr. Thomas Frieden said a full investigation would be conducted into how the infection had occurred.
“Clearly there was a breach in protocol,” he told CBS.
The CDC investigation, he told reporters, would focus on possible breaches made during two “high-risk procedures”, dialysis and respiratory intubation.
Education and training of health workers would be stepped up, he said, and efforts would be made to reduce the number of staff treating Ebola cases.
Dr. Daniel Varga, of the Texas Health Resource, said the health worker had worn a gown, gloves, mask and shield when providing care to Thomas Eric Duncan during his second and final hospital admission.
Following a positive preliminary test for Ebola, follow-up tests on the infected health worker are due to be completed on Sunday, October 12.
Police are guarding the apartment complex where the woman lives in Dallas as decontamination work is carried out.
No details of her identity or position at the hospital have been given, in accordance with family wishes.
Thomas Eric Duncan tested positive in Dallas on September 30, 10 days after arriving on a flight from Monrovia via Brussels.
He had become ill a few days after arriving in the US, and went to the hospital in Dallas with a high fever.
However, despite telling medical staff he had been in Liberia, Thomas Eric Duncan was sent home with painkillers and antibiotics.
Thomas Eric Duncan was later put into an isolation unit at the hospital but died despite being given an experimental drug.
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