The law prevents Jonathan Ross and Russell Brand being made to pay the £150,000 fine imposed on the BBC for their prank phone calls, Ofcom has said.
The media watchdog announced the six-figure penalty earlier this week over the offensive voicemails the pair left for veteran actor Andrew Sachs in a broadcast on Brand's now-defunct Radio 2 show.
Government minister Hazel Blears argued on Saturday the comedians should be made to pay the fine themselves but her suggestion has been dismissed by the media regulator.
An Ofcom spokesman said the fine - issued for the "gratuitously offensive, humiliating and demeaning" phone messages recorded by the pair in October - were "levied against the BBC and not individuals" and "to do so would require a change in the law".
Ms Blears, the communities secretary, had said she was "quite surprised" to learn the BBC would pay the fine.
"The BBC is funded by all of us as licence-payers, so actually, are we having to pay the fine?" she asked on Radio 4's Any Questions.
"Then I thought maybe Jonathan Ross and Russell Brand should pay it. That might be quite a good idea."
However, an Ofcom statement said: "Parliament decided for very serious breaches of our broadcasting rules the BBC would be subject to a maximum fine of £250,000.
"These powers only allow for fines to be levied against the BBC and not individuals, to do so would require a change in the law."
Brand and Radio 2 controller Lesley Douglas resigned over the incident while Ross was suspended from the BBC for three months after thousands complained about their behaviour.