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Writebol was rushed to an Atlanta hospital in August and was discharged later that month after blood and urine tests showed no evidence of the virus. She told "Closing Bell" she is "feeling good."
On Tuesday, the Centers for Disease Control and Prevention confirmed the first case of Ebola in the U.S. The patient, Thomas Eric Duncan, who traveled from Liberia on Sept. 19, is being treated at a Dallas hospital.
Writebol said the patient was likely experiencing fever, weakness and perhaps some vomiting.
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"It just depends on how the virus has attacked his body," she noted.
Duncan began to develop symptoms last Wednesday and went to the hospital two days later, but was sent home. He was admitted on Sunday.
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Writebol said the most important thing doctors should find out is who the patient has been in contact with.
"It's about where people have been and their contacts. Those are very important questions. What kind of symptoms are you having and knowing the symptoms that are part of the Ebola virus," she said.