The Republican, who frequently uses the airport about an hour from his home in Bowling Green, Ky., told The Associated Press in a telephone interview that he asked for another scan but refused to submit to a pat down by airport security.
He said he was "detained" at a small cubicle and couldn't make his flight to Washington for a Senate vote scheduled later in the day.
Paul, the son of Republican presidential candidate Ron Paul, said the situation reflects his long-standing concern that the TSA shouldn't be "spending so much time with people who wouldn't attack us."
TSA spokesman Greg Soule confirmed there was an incident but didn't identify the passenger as Paul.
"When an irregularity is found during the TSA screening process, it must be resolved prior to allowing a passenger to proceed to the secure area of the airport," Soule said in a written statement. "Passengers who refuse to complete the screening process cannot be granted access to the secure area in order to ensure the safety of others traveling."
A TSA official speaking on condition of anonymity in order to discuss internal screening policies said Paul was never detained. The official said an alarm set off when Paul went through routine airport screening, and Paul refused to receive additional screening. People who refuse to go through airport security are not allowed to get on a plane, the official said. Local police escorted Paul out of the screening area, the official said.
Paul went through a millimeter wave machine that uses a generic outline of a body for all passengers. When there is an alarm, TSA officers target the area of the body that triggered the alarm and pat down the passenger, the official said.
Paul told reporters at the airport that he had no idea why his knee raised concerns with TSA. He said he showed his knee to the security agents and doesn't have any medical hardware or issues in the knee.
"There is no problem. It was just a problem with their machine. But this is getting more frequent, and because everybody has to have a pat down it's a problem," Paul said.
Paul said he was in Denver two days ago and allowed to walk through the screener again and avoided the pat down.
He said he didn't want special treatment from TSA because he's a senator. "I think we need to treat everybody with dignity."
The TSA said Paul was allowed to board another flight after a different screening.
In a June 2011 Senate hearing, Paul raised issue with TSA's screening policies and relayed the story of a 6-year-old constituent who was patted down at an airport.
"I feel less safe because you're doing these invasive exams on a six-year-old," Paul said to TSA Administrator John Pistole. "It makes me think you're clueless, you know, that you think she's going to attack our country and that you're not doing your research on the people who would attack our country."
The TSA has since changed its policy for patting down children to reduce the number of times children have to go through the procedure.
Sullivan contributed to this story from Washington, D.C. Writer Roger Alford contributed from Frankfort, Ky.