Tory MP Philip Davies said it was"completely unacceptable" that 52-year-old Mohammed Rafiq Passwala had been given any form of unsupervised leave.
Passwala, of Bradford, was convicted of sex offences in 1996.
He has not been seen since Thursday morning when he left Fieldhead Hospital in Wakefield.
It is thought he could be in hiding in Ravensthorpe or Dewsbury.
After he failed to return to the hospital, which specialises in caring for people with mental health problems, West Yorkshire Police and South West Yorkshire Mental Health Trust appealed for information to help trace him.
Mr Davies, who represents Shipley, said: "It is completely unacceptable that someone who is clearly acknowledged as dangerous should be given any form of unsupervised leave.
"I do not know why this man has not been properly supervised at all times and I have no idea how they could have allowed this to happen.
"The priority should always be the safety of the public. Whatever the reason was I don't think there's a good enough excuse to give him any form of unsupervised leave. People are now at risk".
Senior Bradford Conservative councillor Chris Greaves added: "No doubt some well-meaning psychiatrist who has his or her head firmly in the clouds is responsible.
"I thought the idea of psychiatric hospitals was that they were places of secure accommodation."
Passwala is 5ft 7in, of stocky build with black/grey hair and a full beard.
At the time of his disappearance he was wearing grey-coloured traditional Asian dress.
Police inquiries reveal he may be in the Dewsbury or Ravensthorpe areas.
Members of the public are urged not to approach him but to contact police immediately on 0845 6060606.
A spokeswoman for South West Yorkshire Partnership NHS Foundation Trust said: "We are not able to comment on individual cases due to patient confidentiality.''