The charity says the bill does not provide a common definition of anti-social behaviour, and that this may lead to misunderstandings.
It is worried that the unusual yet harmless behaviour sometimes displayed by people with autistic spectrum disorders, including Asperger's Syndrome, may be misinterpreted as deliberate anti-social conduct.
"We've already had calls from anxious parents concerned that their sons and daughters could be criminalised because of their disability," said the society's director of policy and public affairs, Stuart Notholt.
The charity is urging the Government to stipulate in the bill that people with autism will not be discriminated against.
The National Autism Society's response is one of a number of concerns raised by the voluntary sector following Home Secretary David Blunkett's proposals last week for a strategy to oversee the implementation of the bill.
Crime reduction charity Nacro criticised the lack of a clear definition of anti-social behaviour in the bill. It also fears that the bill will be ineffective because it tries to tackle too many problems, from dispersing groups of young people gathered in public places through to drug and firearms offences. The charity has released an alternative good practice briefing.
Social care charity Turning Point and Napo, the probation union, both accused the Government of missing the point by ignoring the underlying causes of anti-social behaviour.
The Anti-Social Behaviour Bill has been condemned by various sections of the voluntary sector since the White Paper was published in March.
Homelessness charities protested at plans to criminalise begging (Third Sector, 19 March), and a legal investigation on behalf of a coalition of children's charities working with Nacro discovered that many aspects of the bill could breach human rights law (Third Sector 23 July).