Mr Trump's Friday directive put a 120-day hold on allowing refugees into the country, an indefinite ban on refugees from Syria and a 90-day bar on citizens from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
In Malaysia, the group CEO of Asia's largest budget airline, AirAsia, suggested countries in the 10-member Association of Southeast Asian Nations (Asean) could cash in.
"With the world now getting more isolationist, it's time for Asean to start making it easier for tourists to come," Mr Tony Fernandes said in a tweet yesterday.
Malaysia is a popular destination for tourists from the Middle East, with nearly 200,000 arriving last year from countries including the United Arab Emirates, Saudi Arabia, Iraq and Qatar.
In neighbouring Thailand, tourism officials said the US ban could lift visitor numbers.
The Middle East is a big market for us, especially in the medical tourism sector. They may choose to visit Thailand more and this may also boost our sector," Tourism Authority of Thailand Governor Yuthasak Supasorn said.
Mr Trump has presented his ban as a way to protect the US s from Islamist militants, but it has been condemned by a growing list of foreign leaders and drawn protests by tens of thousands in American cities.
With concerns about safety and security building, some Asians were reconsidering US travel plans and seeking alternatives, even though their countries were not subject to the restrictions.
"When you want to travel, especially for leisure, then you want peace of mind," said Ms Alicia Seah, director of public relations and communications at Singapore's Dynasty Travel.
"Right now people are planning for their March-April onwards travel. They will put their travel plans (to the US) on hold at this juncture in time."
Singaporeans may either chose to travel to the US later in the year or explore alternative locations such as Australia, New Zealand, Canada or within Asia, she said.
Mr Trump has argued that tougher vetting of immigrants is needed to protect America from attacks, but critics complain that his order unfairly singles out Muslims and defiles America's historic reputation as a welcoming place for immigrants.
Mr Keysar Trad, president of the Australian Federation of Islamic Councils, said Trump's travel restrictions were not only hurting innocent people but were "bringing great damage to his own economy and to the standings of Americans internationally".
"Everyone who has relatives in America, whether they are from the countries listed or not, they are petrified of what this man is going to do to America and to their relatives," Mr Trad said.
Some education providers had seen early signs of an impact.
Mr Rod Jones, CEO of Australian-listed education firm Navitas Ltd, said the company had seen a downturn in inquiries for their US-based English language courses.
"We have started to see students back off from the US because of their concerns about potential issues they may face," Mr Jones told analysts on an earnings call.
"But they still want to go somewhere," he added, identifying Canada and Australia as important alternatives.
"The Canadian Prime Minister has come out and said 'if the US doesn't want you, we'd love to have you' and I think it is the approach of Australia too."
Ms Aulia Adila, 24, a young professional in the media industry in Jakarta, had been considering the US as an option for postgraduate study.
"When Trump had a chance of winning the election this made me reconsider going to the States to study. Now that he won, and with the Muslim ban and the new migrant policy, it's becoming even more impossible and unsafe to be in America," Ms Adila said.
"I'm considering another country where I'll feel safe."