The Local Government Association (LGA) says the government needs to find "genuinely new money" to meet its funding pledges to schools in England.
Ministers insist money raised from a sugar tax on soft drinks will be spent on improving child health.
But the LGA fears this money is being used to cover funding shortages.
It says schemes to improve pupils' health cannot be seen as "nice-to-do but fundamentally non-essential".
In February, ministers announced that £415m would be pumped into schools, as part of a healthy-pupils capital programme, to pay for facilities that support sport, after-school activities and healthy eating.
This is to be paid for by a levy on soft drinks with the most added sugar, introduced from April 2018.
Last week, Education Secretary Justine Greening announced an extra £1.3 billion for schools over the next two years, a move that came amid concerns from schools and parents about intense and growing pressures on budgets.
Some of this £1.3bn would come from making savings of £315m from the healthy-pupils funding, the Department for Education (DfE) said.
It is understood that the government now expects to receive less money than previously expected from the sugar tax and the Treasury is topping up the fund to the original expectation of about £1bn.
It is understood that it is this part of the money that will now go towards general school funding.
But Izzi Seccombe, chairman of the LGA's community wellbeing board, said:  "It is vital that the soft drinks levy, which marked a significant step in the fight against obesity, is protected.
"Government needs to find genuinely new money to meets its new school funding commitments.
"It is perverse and counterproductive to simply shift this money around, particularly at the expense of children's health."
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Mrs Seccombe added: "The government needs to be clear about what this now means for the levy, and for reducing the worrying levels of child obesity in this country.
"Schemes that encourage physical activity, healthy eating and improve children's mental and physical health - which the levy would have been used to pay for - cannot be seen as nice-to-do but fundamentally non-essential."
A spokeswoman for the Department for Education said: "Our soft drinks industry levy will raise an estimated £775m by 2020 and has led to soft drinks companies cutting sugar levels in their products.
"Every penny of England's share of that money will be spent on improving child health."
Money set aside for promoting physical activity and healthy eating in schools should not be used to "plug a black hole in funding", councils say.