A DUP insider has said party representatives are forced to pay up to £1,000 if they break internal rules on dealing with the media.
The other main Stormont parties have said they do not impose similar penalties.
The DUP said it operated under a constitution and a code of conduct, passed by its executive.
The claim about the fining system emerged in an interview given by an anonymous party representative to Radio Ulster's Nolan Show.
"It was Timothy [Johnson] who sent me the letter," the source said in reference to the DUP chief executive.
"He emailed me and then he sent me a letter saying: 'You've spoke to the BBC (which I did) and we're fining you £100'."
The representative said "lots of people" had been fined and that it was "quite a frequent occurrence."
The representative said that Mr Johnson acted as "God incarnate" within the DUP, saying he was "judge, jury, executioner, implementer, enforcer, adviser".
The representative also said that the DUP is officially boycotting the the Nolan Show due to its coverage of the RHI scandal and that the party tightly controls what MLAs are permitted to say during all media appearances.
A DUP statement said the party operated under a constitution and a code of conduct that had been passed by its executive committee.
The statement said that from "time to time" the chief executive wrote to members on code of conduct matters.
"The party reserves the right to decide what programmes to participate in and the best mix of platforms to ensure ongoing communication with the people of Northern Ireland," it said.
