Most, if not all of them, were notified Wednesday. Duncan, who was admitted to the hospital on Sunday after complaining of a fever and abdominal pain, remains in stable but serious condition. He's the first person to be diagnosed with Ebola in the U.S., and only began showing symptoms after arriving in the country on Sept. 20.
Read MoreEbola vaccine: Why it's taking so long to make one
Separately, Texas health officials have ordered four family members who had contact with the Dallas Ebola patient to stay home and not have visitors to prevent the potential spread of disease.
The order, hand delivered to Thomas Eric Duncan's relatives Wednesday night by Texas Department of Health Services officials, legally requires the family to comply until at least Oct. 19, when the incubation period has passed and the family is no longer at risk of having the disease.
More from NBC News:
Slow response? Ebola victim's nephew says he alerted feds
Ebola patient vomited 'all over,' witness tells Reuters
'Rock solid' dog rescued from tar pit
The order also requires the family to be available to provide blood samples and agree to any testing required by public health officials.
Read MoreCould Ebola fears keep foreign tourists away?
Ebola is not contagious until symptoms appear. The family members do not have symptoms at this time.
Duncan, 42, is the first person to be diagnosed with the killer disease in the United States. He traveled last month from his native Liberia and developed symptoms last week. He initially was sent home from a Dallas hospital and remained at home for two days while showing symptoms.
Read MoreBe wary of the Ebola effect