The PM does “not agree” with the executive order signed on Friday night and will make representations if it hits Britons, a statement from Downing Street said.
Somalia-born Farah lives in America with his family but is thought to be currently training in Ethiopia meaning he may be prevented from returning home.
Zahawi, who is of Iraqi origin but a British citizen, said a US immigration lawyer had confirmed that he would be affected by the ban.
May arrived back in Britain on Saturday night to a storm of fury after she failed three times to answer questions on the controversial US Presidential order during a press conference in Turkey earlier in the day.
She finally said: “The United States is responsible for United States policy on refugees. The UK is responsible for UK policy on refugees.”
MPs from across the political spectrum criticised May for not condemning the ban.
Trump has barred all refugees from entering the US for four months but blocked those from war-ravaged Syria indefinitely as part of a plan to stop “radical Islamic terrorists”.
A 90-day ban on entry to the US from seven Muslim-majority nations has been imposed.
Speaking in the White House, Trump said the ban was “working out very nicely”, reports the Press Association.
He said: “It’s not a Muslim ban but we were totally prepared. It’s working out very nicely.
“You see it at the airports, you see it all over, it’s working out very nicely, and we are going to have a very, very strict ban and we are going to have extreme vetting, which we should have had in this country for many years.”
The legal action named Trump in his official capacity as president, as well as the Department of Homeland Security and other high-ranking officials.
Although temporary, it represents the first constitutional setback faced by the new administration.
Within hours of Trump signing the order on Friday night, stories of how people were already being affected began circulating on social media.
Hundreds of protesters gathered at New York’s John F Kennedy Airport to show their anger at Mr Trump’s ban on refugees entering the United States.
Demonstrators held placards with slogans such as “no hate, no fear”, and shouted chants exhorting “no borders, no nations, no racist deportations”.
The immediate fallout from Trump’s order meant that an untold number of foreign-born U.S. residents now traveling outside the U.S. could be stuck overseas for at least 90 days - despite holding permanent residency “green cards” or other visas.
Some foreign nationals who were allowed to board flights before the order was signed Friday were being detained at U.S. airports, told they were no longer welcome, reports the Associated Press.
In Tehran, Foreign Minister Mohammad Javad Zarif said Iran would stop issuing new visas to U.S. citizens in response to Trump’s ban, but that anyone already with a visa to Iran wouldn’t be turned away.
The Council on American-Islamic Relations said it would challenge the constitutionality of Trump’s order.
“There is no evidence that refugees - the most thoroughly vetted of all people entering our nation - are a threat to national security,” said Lena F. Masri, the group’s national litigation director. “This is an order that is based on bigotry, not reality.”