The data was posted on a procurement website, revealing details such as health conditions and social care needs.
Gloucestershire County Council (GCC) said it had "done everything we can" to remove the online material.
The victims of the breach had been informed and an investigation is under way, the authority added.
The council uses online procurement portals to post notices when urgent residential or non-residential care was needed for people with physical disabilities, learning disabilities or mental health needs.
But staff had attached personal "pen pictures" of adults requiring such urgent help to notices available to the public on the supplyingthesouthwest.org.uk portal, dating from the start of 2017.
The council's chief executive Pete Bungard "sincerely apologised" for the error, and said staff had already been retrained while an internal investigation was carried out.
A spokeswoman for the authority said GCC had "worked with the procurement websites and search engines" and added she was "confident the council has done everything it can to remove the information".
Earlier this year, GCC launched an investigation after it unwittingly revealed details online of a Â£500m contract for a controversial incinerator project.
A council has apologised to 14 vulnerable adults whose personal details were published online.