Posters of Barry Denne have been placed around the town of Magaluf asking for help tracing him after he disappeared on 14 September.
A Kent County Council spokeswoman said Mr Denne was on holiday with one other client.
They were accompanied by two workers from a private care home in Kent.
"This has never happened before to our knowledge and we would obviously want to see if any lessons could be learned."
She said an extensive search had been carried out in Majorca using three helicopters.
Appeals had been broadcast on television and radio.
Kent County Council, which had placed Mr Denne in the private care home, is appealing to tourists who might have seen him to come forward as fears grow for his safety.
An appeal is to be launched today in Britain.
Peter Gilroy, Kent County Council's social services strategic director, said: "We are very concerned.
"Mr Denne seems to have vanished into thin air and we appeal to anybody who thinks they might have seen him to come forward."
Mr Denne is described as 5ft 4in and weighing around seven stone. He has very limited communication and was wearing brown shorts and an orange top when he disappeared.
Kent County Council said it was Mr Denne's third accompanied foreign holiday. He has already visited Portugal and Spain.
Oliver Mills, Kent social services director of operations, flew to Majorca yesterday accompanied by an interpreter to help with the search.
Mr Denne's brother and sister, who claimed they were not being kept properly informed, return from Majorca today after flying out to help with the search.
The council said Mr Denne was with the two care workers when he disappeared at around 11pm in the street in Magaluf.Reuse content