Ross and Brand both apologised for their behaviour
Jonathan Ross and Russell Brand cannot be made to pay the £150,000 BBC fine by law, regulator Ofcom has said.
The media regulator imposed the fine last week over the prank phone calls made on Radio 2 by both comedians.
Communities Secretary Hazel Blears said she thought the stars should be made to pay the penalty themselves.
But an Ofcom spokesman said the fine was "levied against the BBC and not individuals" and "to do so would require a change in the law".
The fine was imposed for what Ofcom called "gratuitously offensive, humiliating and demeaning" prank calls, which were broadcast last October.
On Saturday Ms Blears told BBC Radio 4's Any Questions said she was "quite surprised" to have read the BBC was footing the bill.
"The BBC is funded by all of us as licence-payers, so actually, are we having to pay the fine?"
"Then I thought maybe Jonathan Ross and Russell Brand should pay it. That might be quite a good idea."
Ofcom 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."