The latest alleged incident follows a complaint by Ali that immigration agents detained him for almost two hours at the Fort-Lauderdale International Airport in Florida.
Ali and his mother were in Washington to speak at a forum that was put together by Democrats to discuss President Donald Trump's immigration policy.
In a separate statement, TSA claimed that agents were concerned about a "large piece of jewelry" Ali was wearing.
Ali Jr. told the Sun-Sentinel in a phone interview that he was red-flagged while attempting to board a JetBlue flight headed to Fort Lauderdale, Florida.
TSA spokeswoman Lisa Farbstein said a call was made to confirm Ali Jr.'s identity when he arrived an at an airport check-in counter.
"None of this was happening Wednesday", Mancini told The Washington Post, noting that Ali flew to Washington without incident.
The first order, which temporarily stopped the entry of refugees and travellers from seven Muslim-majority countries, was the subject of more than two dozen lawsuits.
TSA added that it does not have the authority to detain passengers and that Ali Jr. was not detained.
Mr Mancini says he plans to file a complaint with the Department of Homeland Security about the incident, and will be "working towards a lawsuit". "Religiously profiling son of "The Greatest" will not make us safe", she wrote.
She said he also was patted down because his jewellery set off a checkpoint scanner alarm.
According to USA Today, Camacho-Ali said this to lawmakers on Thursday: "Somebody needs to turn this "humanity" switch on because we're not going to go back to Robert E. Lee".
Mr Ali was told by airline staff that his IL identification card was invalid for flying, despite using this document to travel to Washington just two days earlier.
Ali is a Muslim born in Philadelphia and holds a US passport.
During his detention, Ali Jr. was asked repeatedly about his lineage and his name, "as if that was a pre-programmed question that was part of a profile", Mancini said.