Bristol City Council sent an email asking for views on a new support service to hundreds of people.
The names of all the children and the email addresses of their primary carers were viewable to all recipients.
The authority said it was aware of the issue and was investigating.
The email, which has been seen by the BBC, was sent by the disabled children and specialist services department of the council.
A parent, who wished to remain anonymous, and who received one of the emails, said it was "a fundamental breach of trust and data".
"It really signifies the disdain that they have for families with disabled children.
"It's such a lack of concern for us. I feel this really exemplifies their indifference to the plight of disabled children in Bristol."
She said there were 487 names of children and their carers visible on the email she received, and those names were all between "H and L" alphabetically, "so there will be a lot more".
"Ironically, it's about a survey that they want us to fill in to tell them how they can improve their services.
"It's very difficult to put into words how ridiculous and unnecessary it is," she added.
The Information Commissioner's Office (ICO), which investigates data breaches and can fine serious offenders, said it had not yet heard from the council, but pointed out the authority had 72 hours to report any breach.
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