'Queen made me knight, Trump made me alien': Farah
He said according to the new rules it would keep the Somali origin athlete apart from his family who are based in the US.
Farah compared the treatment of Muslim-Americans by Trump to the recognition bestowed on the Muslim athlete by Queen Elizabeth earlier this month.
"On 1st January this year, Her Majesty The Queen made me a Knight of the Realm. On 27th January, President Donald Trump seems to have made me an alien," Farah said in a statement on his Facebook page.
"It's deeply troubling," the 33-year-old said, "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."
Farah was born in Somalia, one of seven predominantly Muslim nations subject to the executive order signed by Trump that temporarily bans entry to the US.
Speaking from Ethiopia, where he is currently training, Farah said he is deeply troubled about the impact the law could have on his family who are based in Portland, Oregon.
The UK's Press Association is reporting that Farah and his representatives are trying to establish whether the fact he was born in Somalia will now present a problem for him when he wishes to return to the US.
Farah does not have dual nationality or hold a Somalian passport.
He moved to the UK at the age of eight and is now regarded as one of the greatest-ever athletes in British sport after winning the 5,000 metres and 10,000 metres at both the 2012 and 2016 Olympic Games and at the 2013 and '15 world championships.
He also won the 5,000 metres gold at the 2011 world championships and was recently given a knighthood by Queen Elizabeth II.
Agencies contributed to this report.