The younger Fury was due to face off against the social media star ahead of their rescheduled grudge match after the event was last week officially confirmed for August 6 at Madison Square Garden.
Tommy, who rose to fame during the 2019 season of Love Island when he and his influencer girlfriend Molly-Mae Hague made it to the final of the reality series, posted a message expressing his concerns after he was stopped from flying.
Speaking on Instagram, he said: "Me and my team arrived at Heathrow Airport ready to fly out and as soon as I entered the airport I was pulled to one side and told by a Homeland Security officer that my ESTA had been denied and that I wasn't able to travel to the USA for a reason I apparently know.
"I can stand here and say I have done nothing wrong and I have no clue why I'm not allowed to travel to the USA. I've been training for a fight this whole time and that's all I've been doing. I have no clue why I'm not allowed to travel and neither does my team or my lawyers.”
He adds: "Now I've got to go to the embassy trying to resolve it and I'm in the middle of training. I don't know why this has happened a huge shock to me and my team. It's government issues and it's a lot bigger than the fight right now and I'm trying to get it sorted."
Tommy’s dad John previously admitted he and other members of Tommy’s team were banned from entering the US due to Tyson’s links to mob boss Daniel Kinahan.
And the ‘Gypsy King’ himself made headlines when he was refused entry into the United States as a result of the sanctions against the Kinahan Organised Crime Group.
While none of the Furys have any association with crime, the travel bans are now said to potentially jeopardise the career of both fighters.
Jake Paul and Tommy were due to spar last December but Tommy was forced to pull out due to injury.
Jake later took to Twitter to demand Tommy fight him on August 6 in Madison Square Garden.
“Tommy Fury, you pulled out last year,” he wrote. “Then you agree to fight me now but your dad is trying to pull you out again?
“We’ve given you everything you asked for — $2 million purse, VADA testing, tampons. You have 24 hours to clear this up or I will never give you this opportunity again.”
Responding, John Fury said: “We want this fight with you Jake, because we know we can beat you mate.” John then offers to take “less money” to hold the fight in any other country.
"If you want this fight my friend, you’ve got it. But we can’t take it in America. But we will negotiate less money to fight elsewhere in the world, yeah?
"You can have it on the sixth of August but it’s got to be not in America because all us (sic), I’ll be honest with you, are suspended and banned for life, I can’t get to you at all, Tyson can’t get to you because he’s got a few issues at the moment so Tommy’s got no team.”
Despite posting social media pictures of himself in Miami in recent weeks, Tyson Fury has not entered the US since his former fight fixer Daniel Kinahan was sanctioned by the US Treasury in April.
Over 600 people, including the world heavyweight champion, are banned from entering the US at present because of their direct association with drug boss Daniel Kinahan.