Google has recalled travelling staff members to the US after an executive order from President Donald Trump restricting entry for nationals of seven Muslim-majority countries.
Syrian refugees are banned from entry until further notice.
Visas for nationals of six countries, including Iran and Iraq, will not be issued for the next three months.
Google has told the BBC it is concerned about the order and any measures which could block great talent from the US.
The BBC’s business correspondent Joe Lynam says President Trump’s order means that thousands of citizens from Iran, Iraq, Syria, Yemen, Sudan, Somalia and Libya may not be allowed to board flights bound for the US – even if they hold a so-called “green card” (permanent residents’ permit).
Mr Trump said the measure would “keep radical Islamic terrorists out of the US”.
But rights groups say there is no link between Syrian refugees in the US and terrorism.
There are already reports of travellers from the countries targeted being turned away as they try to board flights to the US.
The American-Arab Anti-Discrimination Committee said this appeared to include “green card holders and other visa holders”.
It advised nationals from the affected countries but living in the US not to travel abroad.
Some Republicans have welcomed Mr Trump’s announcement, including the Speaker of the House of Representatives, Paul Ryan, who said it was “time to re-evaluate and strengthen the visa vetting process”.
The new policy is also affecting visits from relatives.
An Iraqi journalist living in the US, Mohammed al-Rawi, posted on Facebook, saying his father had been turned away from a Los Angeles-bound flight in Qatar.
Jamal Abdi from the National Iranian American Council told the investigative journalism organisation Pro Publica: “We are inundated with calls and questions of how this is going to affect people.”
The Council on American Islamic Relations says it will file a lawsuit against the executive order.
Silicon Valley, where many employed in the technology industry are of non-US origin, is also worried.
Facebook founder Mark Zuckerberg posted a lengthy note, saying he was “concerned” about the president’s executive orders, and noting that he, like many Americans, is the descendant of immigrants