Trump posted a series of tweets saying, people who go to "faraway places to help out are great," but must "suffer the consequences" for their actions.
Dr Kent Brantly and Nancy Writebol, both contracted the disease while treating patients in Liberia.
They will be treated in isolation, and officials say their return will not put Americans at risk.
Trump was not convinced though, tweeting; KEEP THEM OUT OF HERE."
More than 880 people have been killed by the virus across 4 West African countries since the outbreak began,’’
The survival rate is low – and there is no cure.
The reaction by Trump cpomes as a man was admitted to a New York City hospital Monday suffering from symptoms similar to those of Ebola and was being tested to see if he was infected, hospital officials said.
"In the early morning hours of Monday, August 4, 2014, a male patient with high fever and gastrointestinal symptoms presented at The Mount Sinai Hospital's Emergency Department in New York City," a hospital statement said.
The patient recently traveled to a West African country where Ebola has been reported, it added without naming the country.
"The patient has been placed in strict isolation and is undergoing medical screenings to determine the cause of his symptoms. All necessary steps are being taken to ensure the safety of all patients, visitors and staff," the hospital added.
According to an updated statement Monday by the UN World Health Organization, at least 887 people have died from Ebola since the beginning of the year, after the virus spread across Guinea, Liberia and Sierra Leone.
Ebola-like symptoms include fever, vomiting, severe headaches and muscular pain and, in the final stages, profuse bleeding.
Kent Brantly, the US doctor infected with the virus, "seems to be improving," the director of the Atlanta-based Centers for Disease Control, where he is being treated in an isolation unit, said on Sunday.
A second American infected with the virus while working in Liberia is due to arrive back in the United States on Tuesday.
The Christian missionary group SIM USA said Nancy Writebol, 60, was in a "serious but stable condition" and was "expected to return to the US for further treatment on Tuesday".
She will be evacuated on the same plane that carried Dr Brantly, and will also be taken to the isolation unit in Atlanta.
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