The confrontation was provoked by a story that Professional Pensions, published by Incisive Media, carried on the front page of last week's issue.
The story was written by Jenna Towler and concerns the removal of pension schemes from a Nottingham-based pension trustee called GP Noble.
The Pensions Regulator objected to the story on the grounds that it carried restricted information, the publication of which is prohibited under the Pensions Act 2004.
It wrote to the editor-in-chief of Professional Pensions complaining, and Incisive said a member of The Pensions Regulator staff phoned Towler to complain about the piece, telling her that she could go to prison for publishing it.
The regulator asked Professional Pensions not to publish any more stories about GP Noble and to "confirm from whom you received all of the information which relates to our regulator involvement".
Incisive Media has responded through its lawyers, Carter Ruck, arguing that the article does not carry restricted information. It says that the Pensions Regulator's actions leave it with "little choice" but to explain the matter to readers, adding that therefore it will follow up the story.
The letter from Carter Ruck also rejects the request to reveal the source of the story.
David Worsfold, group editorial services director at Incisive Media, said: "We are determined to fight this outrageous threat to the freedom of the press and the right of journalists to keep their sources confidential.
"This is just another example of how the UK government keeps giving unelected bodies the (apparent) right to shackle the press and undermine the cornerstones of press freedom, such as the right to keep sources confidential."
A regulator spokesperson said: "The Pensions Regulator takes an open and transparent approach, but in certain instances information is protected in law to protect the confidentiality of those who we regulate, and avoid jeopardising investigations."