The LGA, which represents councils in England and Wales, said there had been a “spate of accidents” recently.
And it said councils “urgently need tougher powers” to tackle the issue.
But the government said police already had the “necessary power to take action” and it had “no plans” to give local authorities more powers.
Driving a lorry into a road where it breaks height or weight restrictions is punishable with a fixed penalty notice of £50 - though serious cases can go to court, where penalties can be much higher.
Local authorities in Wales and London have been given powers to use against lorry drivers who break the law, the LGA said.
It said police did not always have the resources to enforce road weight and width restrictions, so all councils must be given powers to do so.