Dr Samira Asgari, a postdoctoral fellow at the Swiss federal technology institute EPFL in Lausanne, was due to fly to Boston on Saturday to take up a post at the laboratory of Dr Soumya Raychaudhuri, a professor of medicine and biomedical informatics at Harvard Medical School.
The lab carries out research into cures for tuberculosis, diabetes and rheumatoid arthritis, according to The Boston Globe.
Dr Asgari has a two-year funding grant for her research from the Swiss National Science Foundation.
After flying from Geneva to Frankfurt, she was then told she could not board the connecting flight to Boston even though she had a valid visa, reported Blick.
Speaking to the Swiss paper, Dr Asgari said “I was totally shocked”.
“I feel extremely unjustly treated. Because of my citizenship I am discriminated against.”
Talking to The Boston Globe Dr Raychaudhuri said he “couldn't believe that somebody with a visa with her standing would be denied entry”.
Trump's executive order, signed on Friday, temporarily barred citizens of seven Muslim-majority countries (Iraq, Syria, Iran, Libya, Somalia, Sudan and Yemen) from entering the US. It also indefinitely banned all Syrian refugees and suspended the US refugee admissions programme.
The ban could affect some 31,000 people living in Switzerland, according to Swiss media, quoting official residency statistics.
At the end of 2015 there were more than 10,600 Syrians living in Switzerland, as well as over 7,000 Iraqis, nearly 7,000 Somalis and 4,500 Iranians, said 20 Minuten.
Some of these are likely to be people who have requested asylum in Switzerland, who are generally unable to travel abroad in any case.
Speaking to 20 Minutes, a spokeswomen for Swiss International Air Lines said another woman was denied entry after flying from Geneva to New York on Saturday.
She returned to Switzerland on the next flight, at the airline's cost.
Swiss was also forced to cancel two flights carrying refugees to the US for the International Organization for Migration, added the spokeswoman.