Yorke, who had worked the previous day for BeIN Sports as a pundit on United's UEFA Europa League win over French club St Etienne, confirmed the story to Sky Sports after colleague Richard Keys tweeted the news.
The Iranian stamp in Yorke's passport related to him playing in a charity match in Tehran, in 2015.
That charity match in Tehran featured Yorke on a World Stars team that also included Luis Figo, Roberto Carlos, Fabio Cannavaro, Marcel Desailly and Edgar Davids.
"I couldn't quite believe what was happening" Yorke told The Sun.
"I have lost count of the number of times I have been to America, I love the country, yet I was being made to feel like a criminal.
"I had bought my ticket and checked in and was about to get on the flight when I was stopped by two officials. I thought 'what is happening here?'.
"They told me there was a visa problem and a red flag had come up against my name because of an Iranian stamp in my passport. I went there to play in a legends match to open a stadium and didn't even stay overnight.
"The two officials told me if I got on the flight I would simply be deported back to Qatar once I arrived in the States. I tried to explain I didn't even live in Qatar and was just trying to get to my home in the Caribbean."
US President Donald Trump had issued an executive order banning travellers from seven Muslim-majority countries, including Iran, from entering the US for 90 days.
The ban has since been suspended in a series of court rulings for constitutional reasons but Yorke still claims to have been prevented from entering the country.