The Japanese driver revealed he was delayed by as much as three hours as officials quizzed him over the reason for his visit.
“They let me in after a couple of discussions, well, a lot of discussions,” he confessed.
“Actually, I nearly got sent back home.
“Everything [is] all good now… luckily I’m here now.”
Tsunoda had the appropriate visa to enter the country as he was left clueless for the additional interest he received.
Formula 1 was only last in the United States in October for the United States Grand Prix and was in Miami in April.
On neither occasion did the 24-year-old face issues entering the country.
“Yeah I had the visas and everything, been the same I guess the last three tracks right, was able to enter smoothly previous tracks,” Tsunoda said.
“It felt a bit strange I got stopped and had a proper discussion. Luckily it didn’t go more than two or three hours.
“But yeah I felt… it’s going to be a long travel for me.”
Travelling with his physio, Tsunoda was ushered into an interrogation room where he was not allowed contact with his travelling companions, employer, or even representatives of Formula 1.
“Obviously when you have questions and go to customs you go individually,” he explained.
“I went to the room, he put me in the room and we had a conversation even like can I bring the person that travel with and maybe he can help a little bit to explain a bit more about myself and the situation in Formula 1.
“But they didn’t allow me to bring that friend or even call anything.
“I wanted to call to the team or Formula 1 that can help me, but in that room you can’t do anything.
“I was wearing like a pyjama so maybe I didn’t look like a Formula 1 driver,” he added.
“I got a lot of pressure from them, but I was like, I couldn’t say anything otherwise, if I say something, I feel like I’m more in trouble.”
Eventually the matter was settled and Tsunoda was free to enter the country and compete in F1 for the ninth time in the United States.
Track action for this weekend’s event begins on Thursday evening local time (13:30 AEDT Friday).