The Metropolitan Police confirmed it had received a report on Oct 18 of malicious communications and threats to kill towards an MP in relation to a video posted on social media.
A force spokesman said a man had been detained in Dover on Thursday for immigration offences.
Detectives have launched an investigation and the Met is liaising with partners from Border Force.
A statement from the force said: “The Met takes the safety and security of MPs extremely seriously and we are committed to ensuring that they, their families and staff can go about their work and lives without feeling unsafe or intimidated.
“As part of Operation Bridger, the national policing operation that coordinates protective security advice, we work closely with the parliamentary authorities, local forces and the Cabinet Office in ensuring that the appropriate security measures are in place for all MPs.”
The Reform UK leader shared a video on X, formerly Twitter, purporting to be of the illegal immigrant crossing the English Channel on a packed boat on Thursday morning.
Mr Farage told The Telegraph: “This man will be of no benefit to our country. He should be deported immediately.
“He brandishes regularly on TikTok pictures of him with guns, drugs, he’s threatened to kill a Member of Parliament and here he is.
“This BBC idea is that these are all poor desperate people, I’m sorry, a lot of them are very aggressive young men.
“This highlights what is happening in the Channel, it is a national security emergency.”
Asked how he had personally felt about threats being made on his life, Mr Farage, 60, replied: “I’m not exactly thrilled, of course, I’m not. I have a very, very deep worry that this man’s going to be here for the rest of his life.”
The Home Office has been approached for comment.