The family of 26-year-old Nina Pham, a nurse at the Texas Health Presbyterian Hospital in Dallas, provided the information to news sources on Monday.
Pham contracted the virus after treating Liberian patient Thomas Eric Duncan, who succumbed to the virus last week in Dallas.
Duncan had contracted the disease in Liberia a month ago and was the first person to be diagnosed with Ebola in the US.
The director for the Centers for Disease Control in Atlanta, Tom Frieden, had previously said the Dallas Ebola infection was due to a breach of safety protocols.
But according to reports that came out later, Pham was wearing protective gear whenever she had contact with Duncan. She had been self-monitoring and was hospitalized upon developing Ebola-like symptoms.