Up to 200 surnames were published on Portsmouth City Council's website.
The council said an error meant information was presented in a "different format" but claimed it was not possible to "identify individuals".
The Information Commissioner has been informed of the breach by the council.
Once a month the council must list all its spending over Â£500 and the latest report included care and drug rehabilitation payments made to individuals, along with their surname, care home and clinic.
The breach was spotted on Friday and the details were removed "as soon as possible", the council said.
Michael Lawther, Portsmouth City Council's senior information risk officer, said: "We are confident only a very small number of people accessed the file before it was removed and will be contacting them to ensure the information is destroyed.
"We treat data protection with the utmost seriousness and as a precaution have informed the Information Commissioner's Office of what has happened."
A spokeswoman for the Information Commissioner's Office (ICO) said: "We're aware of an incident at Portsmouth City Council and are considering our next steps."
Personal details of people under social care and drug rehabilitation services have been released online in an apparent data breach.