The 31-year-old was preparing for a work trip with environmental group Oceana in the next few days, but her request to enter the country was blocked by US authorities, the Daily Mail has reported.
It is believed her trip last year to Somaliland, which the US recognises as part of Somalia, could have played a part.
Such travel woes could be embarrassing for her partner, who is due to meet US President Donald Trump at the G7 summit in France over the weekend.
Before travelling to America, UK citizens can apply for an Electronic System for Travel Authorization (ESTA), which allows travel to the country for up to 90 days without having to apply for a visa.
But those who have visited Somalia since March 2011 may not be eligible for an ESTA and could have their request refused, according to the US Embassy and Consulates website.
Despite being denied, a person can then go through the normal process of applying for a visa. It was not clear if Ms Symonds had applied for an ESTA.
Nimco Ali, Ms Symonds’ travel partner last year, responded to reports of the travel issue by saying that Somaliland was “Africa’s best kept secret”.
She added: “For 28 years without international assistance we have rebuilt our Country and are the only democracy in the Horn of Africa. I am happy to personally show anyone around the land I was sourced from.”
Ayan Mahamoud, head of the Somaliland Mission to the UK, said it is a “peaceful and stable” state which “continues to suffer the consequences of non-recognition”.
She added: “US visa restrictions often deter UK nationals from travelling to Somaliland; and our citizens – both at home and abroad – face significant travel restrictions.
“This impacts freedom of movement, harms our economy and risks deterring investors.”
Ms Symonds, who lives at Downing Street, holds no official role and is not supported by taxpayers. Downing Street has declined to comment on her visa issue.