Currently they receive £55m a year in extra funding in recognition of the extra costs they incur recruiting specialist staff, but this is set to end after the 2019/20 financial year.
A survey of 56 councils by the Local Government Association found that 61 per cent believe that maintained nurseries in their area could close if this funding is not protected. Of those surveyed 19 (33 per cent) said it was "very likely" that nurseries would close in their area without funding protection.
Just over half (52 per cent) believe the loss of this extra funding will mean reduced support for children with SEND.
The LGA is calling for the extra funding to continue into 2020/21 and for a long-term funding package arranged as part of the next spending review, which is planned for next year. It is also calling on the government to improve funding for SEND provision in schools.
Latest government statistics show that more than 5,000 children with SEND currently attend England's 397 maintained nurseries.
The proportion of SEND children at maintained nurseries is 12.8 per cent, compared with a rate of 6.3 per cent of three- and four-year-olds in the general population having SEND.
"As our survey shows, councils have grave concerns about the future of maintained nursery schools if the current funding does not continue beyond 2020," said Anntoinette Bramble, LGA children and young people board chair.
"This could have a detrimental impact on children with special educational needs, for whom maintained nurseries provide a lifeline of vital support.
"For example, unlike other nurseries, maintained nurseries have to have a qualified teacher designated as a SEND co-ordinator.
"This provision is now under threat unless government commits to an extra year of funding in 2020/21 as part of wider work to find a long-term sustainable funding solution in the Spending Review.
"This is on top of the overarching funding pressures councils are facing in providing support for children with SEND, which we would like to see the Chancellor address in next week's Autumn Budget."
Neil Leitch, chief executive of the Pre-school Learning Alliance, called on the government to ensure that all early years settings are properly funded so that they can effectively support SEND children.
"It is absolutely vital that these children have the same access to quality early years provision as their peers - and yet we know that providing the quality care and support that children with SEND need often comes at a significant cost to providers," he said.
"This is true for 397 maintained nursery schools currently operating across the country, but it is equally true for the 60,000-odd private and voluntary pre-schools, nurseries and childminders providing the majority of places for the 85,000 two-, three- and four-year-olds in England estimated to have SEND.
"That's why it is so important that the Department for Education ensures that it is funding all early years providers adequately - and that is simply not the case at the moment."
Research published last month as part of the ongoing Study of Early Education and Development (SEED) found that spending more time in good-quality early years settings helps children develop emotional skills and build positive relationships with others.
Responding to the survey, children's minister Nadhim Zahawi said: "Children with additional needs should have exactly the same access to early education as every other child.
"That is why we are supporting councils and childcare providers to provide the right support for children with SEND through our Disability Access Fund, worth £12.5m, and the early years national funding formula, which means councils must direct more funding to where need is higher.
"This is on top of the £6bn of funding specifically for children with more complex special educational needs and disabilities."
"Maintained nursery schools make a valuable contribution to improving the lives of some of our most disadvantaged children, alongside wider government support including our free childcare offer for two-year-olds - that's why we are providing local authorities with around £60m a year up until 2020 to protect maintained nursery schools funding.
"I regularly meet with maintained nursery school leaders and we continue to work closely together to better understand the value these nurseries offer, so I would urge councils not to make premature decisions on the future of these nurseries as this work continues."