Stephen Munden, 54, has not been seen since leaving the independent hospital at Winchfield, near Hook, on Tuesday.
He received a hospital order in 2014 after being convicted for possessing indecent images of children and sexual assault on a child under 13.
Police said they were trying to trace him as a "matter of urgency".
A hunt is under way for a sex offender who has gone missing from the Hampshire hospital he was detained at after being convicted of child sex offences.