The boy was apparently held by authorities after arriving from Iran with another family at Dulles International Airport in Virginia, only 25 miles from Washington D.C.
Footage from Washington channel ABC7 shows an emotional woman, reported to be the child’s mother, embracing her son after she was forced to wait anxiously for him to be released by immigration control.
The woman is then filmed singing “happy birthday” in English to the child as she hugs and kisses him.
The woman declined to speak to reporters after the incident and the family's immigration status is not known.
The incident comes amid furious backlash in the US and around the world following Mr Trump’s order which temporarily bars entrance to the US for citizens from seven predominantly Muslim countries, including Iran, as well as indefinitely banning all refugees.
The order also introduces a blanket ban of all Syrian refugees until “sufficient changes” have been made to the US refugee program, without giving further details.
The order states that once refugee admissions resume, fewer will be allowed in. The 2017 cap was set at 50,000 people, compared to 85,000 allowed by President Barack Obama in 2016.
Demonstrators gathered at many US airports, including Dulles, to show their support for refugees and others coming from the banned countries, which are all predominantly Muslim.
They held “refugees welcome” signs and chanted slogans in support of those being detained on arrival by authorities.
A federal judge temporarily halted part of the order, but the majority of it remains in place, with protests taking place at airports around the country.
The move has been denounced by civil rights groups, including the UN’s refugee agency (UNHCR) and the International Organisation for Migration who said: “The needs of refugees and migrants worldwide has never been greater and the US resettlement program is one of the most important in the world.
“The longstanding US policy of welcoming refugees has created a win-win situation: it has saved the lives of some of the most vulnerable people in the world who have in turn enriched and strengthened their new societies."