Overweight or unhealthy people who refuse to attend exercise sessions could have their benefits slashed, in a move proposed by Westminster Council.
GPs would also be allowed to prescribe leisure activities such as swimming and fitness classes under the idea.
The Tory-controlled council said the aim was to save £5bn from the NHS budget when local authorities take over public health provision from April.
BMA member and GP Dr Lawrence Buckman called the idea "draconian and silly".
The measures are contained in a report entitled A Dose of Localism: The Role of Council in Public Health, in a link-up between Westminster Council and the Local Government Information Unit (LGiU).
Under the proposals, overweight benefit claimants could have their money docked if they refuse exercise regimes prescribed by doctors.
Smart cards would be brought in to monitor the use of leisure centres, meaning local authorities could reduce welfare payments for those who fail to follow their GP's advice.
Resident, housing and council tax benefit payments "could be varied to reward or incentivise residents", the report said.
It claims "early intervention techniques" could help save more lives and money.
These include linking welfare payments to healthy lifestyles and rewarding those who take responsibility for their own health, the report's authors claim.
Red tape would be cut for "non-alcoholic venues" to encourage a more responsible approach to drinking, which the report says was promised but never delivered by the change to 24-hour licensing laws.
British Medical Association GP committee chairman Dr Buckman, a GP in north London, called the proposals "some of the silliest things I've heard in a long time".
"When I was first told about this I thought it was a joke," he said.
He added: "The best way [councils] can intervene is to stop restaurants and fast-food chains providing the kind of food that make people put on weight, and interfere with the way foods are sold in shops."
Obesity support organisation Big Matters spokeswoman Susannah Gilbert said: "It would be fairer to use the money to support people rather than to penalise people.
"Any plans for health should be holistic," she added. "Some people have emotional issues to do with food.
"A fast-food generation need support in the long term."
But Jonathan Carr-West, acting chief executive of the LGiU, said the proposals offered "a win-win" solution.
He said the proposals were about "finding innovative ways to both improve people's lives so they don't suffer from these conditions, while also saving money for the public purse".
"We have to look at ways of managing demand, of helping people not to need such expensive health interventions," he said.
He said the proposals would "help people lead healthier, happier lives".
Westminster council leader Philippa Roe said: "This report contains exactly the sort of bright, forward-thinking and radical ideas that need to be looked at.
"The potential improvements to the nation's health and to the public purse could be significant."
But the change to local authority control over public health has led many councils to voice concerns about how much money they will get and the formula that central government will use to allocate funding.
The public health funding announcement was originally expected on 19 December.