A spokesperson for Qatar Airways said it would only carry passengers to the US who had the correct documentation.
"We are enforcing the new rules," said the official.
"If travellers to the US don't have the proper documentation, we are not going to take them to the US."
The news comes after Trump imposed tough new controls on travellers from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
Abu Dhabi-based Etihad Airways said it will apply restrictions on its US routes "effective immediately".
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Qatar Airways also posted a "travel alert" online today, listing the paperwork required by citizens of the seven countries.
These included the "Green Card" and government and diplomatic visas.
Both Qatar Airways and Etihad Airways fly of New York, Chicago, Los Angeles, San Francisco, Washington DC and Dallas. The Qatari carrier also flies to nine other US destinations, including Atlanta.
The newly inaugurated US president signed a sweeping executive order yesterday to suspend refugee arrivals and impose tough controls on travellers from the seven countries.