The 33-year-old holds a dual British-Somali nationality and is a practicing Muslim who has lived in America with his family for the past six years.
He says the new rules are "deeply troubling" and fears under the strict new rules announced by Mr Trump on Friday (January 27) he may not be welcome.
In a statement Sir Mo Farah said: "I am a British citizen who has lived in America for the past six years - working hard, contributing to society, paying my taxes and bringing up our four children in the place they now call home.
"Now, me and many others like me are being told that we may not be welcome.
"It’s deeply troubling that I will have to tell my children that Daddy might not be able to come home - to explain why the President has introduced a policy that comes from a place of ignorance and prejudice."
The new ban means no visas will be issued to nationals from Syria, Iran, Iraq, Libya, Somalia, Sudan and Yemen for 90 days.
It has also emerged Brits holding dual passports which include one of those countries could also be barred from entering America.
This would effectively mean the distance runner who is currently training in Ethopia cannot enter the US.
At the age of eight Sir Mo came over to Britain from Somalia, attending schools in the borough of Hounslow.
His rise to fame came in the London 2012 and Rio 2016 Olympic Games with his double gold medal wins.
He and wife Rhianna and their four children moved to Portland, Oregon, and he recently received the greatest British honour of a knighthood.
He added: "My story is an example of what can happen when you follow polices of compassion and understanding, not hate and isolation."
Mayor of London Sadiq Khan added the move by President Trump is "shameful and cruel."
Mr Khan continued: "The USA has a proud history of welcoming and resettling refugees.
"The President can't just turn his back on this global crisis - all countries need to play their part.
"While every country has the right to set its own immigration policies, this new policy flies in the face of the values of freedom and tolerance that the USA was built upon."
Prime Minister Theresa May has now said the government "does not agree" with the refugee ban inflicted by Mr Trump.