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.
President Trump's order could mean that thousands of citizens from Iran, Iraq, Syria, Yemen, Sudan, Somalia and Libya may not be allowed to board flights bound for the US.
The new restrictions will have a major impact on technology companies that hire skilled staff from all over the world on special H1-B visas.
There have already been reports of "green card" holders, who are allowed to work in the US, being prevented from getting on flights. However, green cards are not specifically mentioned in the executive order.
Mr Trump said the measures detailed in his executive order 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.