The plea was made following a spate of heavy goods vehicles (HGVs) causing chaos on routes where they exceeded the weight or height limit.
Lorry sat-navs are slightly more expensive than regular devices, and include information on bridge heights and narrow roads.
They also allow drivers to enter the dimensions of their vehicle to ensure they are instructed to follow suitable routes.
The Local Government Association (LGA), representing more than 370 councils in England and Wales, wants legislation brought in to make it compulsory for all lorry drivers who use sat-navs to use commercial devices.
Rail services on a commuter line on the outskirts of Birmingham were delayed on Monday after a lorry smashed into a bridge, ripping the roof off its trailer.
Network Rail figures show there were more than 1,700 such incidents in Britain during 2015/16.
A historic bridge in Marlow, Buckinghamshire, was closed for months after it was driven over by a lorry more than 10 times heavier than the structure’s weight limit in September last year.
Residents in Bridgnorth, Shropshire, reported chaotic scenes when a lorry got stuck after being driven through the town’s main shopping street in October.
Lorries of a certain weight or width are banned from many minor roads, but police forces often do not have the resources to enforce the restrictions.
Local authorities in Wales and London have the power to take action if lorry drivers break the law, but councils are urging the Government to roll this out across the whole of England.
The LGA said the money raised from fines could be put towards tackling the backlog in fixing potholes, which could reach an estimated £14 billion over the next two years.
It added that a number of councils are already working with freight and haulage firms to ensure lorries use the most suitable routes.
LGA transport spokesman Martin Tett said that although most lorry drivers are reputable, some rural communities are “fed up” with those who ignore weight restrictions as the additional noise, vibrations and pollution “make their lives miserable”.
Mr Tett called on the Government to “start taking this issue more seriously” and give councils the legislative tools to help their communities and other motorists.
He added: “It is common sense that all lorry drivers should use sat-navs designed for trucks, but this is only going to become a reality when it is a mandatory requirement. We are talking about a very small extra cost to drivers.”
An AA spokesman called on councils to ensure warning signs are clearly visible.
He said: “If a particular road has a particular problem then it’s up to the local authority to come up with the signage to deal with that. And obviously if the lorry or any other road user contravenes that road order and that signage then they are open to a penalty.”