She had applied for permission to enter the country in the next few days as part of her role at Oceana, an environmental group, but the request was blocked by American officials, the Daily Mail reported.
It could become a source of embarrassment for Mr Johnson, who is due to meet Donald Trump at the G7 summit in France at the weekend.
The difficulty with Ms Symonds’ travel plans may be linked to a journey she made to Somaliland last year alongside her friend Nimco Ali, who campaigns against female genital mutilation.
The US does not recognise Somaliland as an independent country, categorising it instead as part of Somalia.
British applicants using the electronic system for travel authorisation (Esta) scheme, which lets them spend up to 90 days in the US without a full visa, are asked whether they have visited Somalia since March 2011.
After Ms Symonds’ travel problems were reported, Ms Ali said on Twitter: “Somaliland is Africa’s best kept secret, it’s my birth place and it’s stunning.
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“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.”
Ms Symonds has no official role in Number 10 and no taxpayer-funded support, although she has been pictured at functions in Downing Street with Mr Johnson.
Ms Symonds and Downing Street officials declined to comment.
Additional reporting by Press Association.