Under the Localism Bill the Government could force authorities to contribute to any EU fines if an act or omission by the council contributed to the penalty being imposed.
Councils are worried that environmental fines are the biggest threat as many authorities are concerned about missing waste and carbon footprint targets.
It comes as fears mount about budget cuts and EU leaders agreed last week to set up a mechanism to bail out any member state whose debt problems threaten the eurozone.
Coun Anne Hawkesworth, leader of Bradford Council's Tory group, is complaining to Communities Secretary Eric Pickles about the plans and will urge that the Bill is amended.
"At a time when council spending is being significantly reduced and many people are worried about their financial security, I am confident that local residents would object strongly to any increase in council tax to pay fines to the EU for a failure to hit their targets," she said.
"There is already a public perception that whilst the UK complies with EU directives, many other member countries do not. Couple this with the fact that some countries have recently been bailed out by countries including the UK and I would imagine any increase in council tax attributable to paying fines to the EU would cause resentment towards the UK's continued membership."
Bob Neill, Minister for Local Government, said if fines are passed on, it can be blamed on former Prime Minister Gordon Brown signing up to the Lisbon Treaty.
He added: "Where these fines are solely due to the fault of a local authority, the burden should fall on the responsible authority not the general taxpayer. Localism cuts both ways – more powers but more responsibility.
"The new Government equally will be stopping the gold-plating of EU regulations which imposes so much extra cost on councils and local firms."
The Local Government Association (LGA) has criticised the clause, saying it would be impossible to fairly attribute liability to councils, making it "unfair and unworkable".
A spokesman said: "The EU treaty clearly states that only governments are liable for fines.
This measure, which has been imposed without any consultation with the sector, imposes a new regime for the government to impose fines extra-judicially, by executive action. It will result in significant and unjustified financial strain on local authorities that are already facing extremely testing circumstances."
The Bill said the Secretary of State must publish a policy statement to set out general principles on how the powers will be used and a minister who makes the order must give a warning notice to the authority.
But Coun Hawkesworth added: "There are already certain fines that the EU can levy directly against councils, so I will be requesting clarification of whether this even amounts to fines on top of fines.
"That Gordon Brown chose to sign the Lisbon Treaty when it can potentially be used as a vehicle to increase the EU's revenue by taking money for fines from council tax is an outrage.
"What would we be paying for? I dread to think that Bradford residents' hard-earned cash could be used to pay for all sorts of crazy schemes in other EU countries."
A spokesman for LGA deputy chairman David Parsons said he will be lobbying the DCLG and Mr Pickles on behalf of councils.