The 28-year-old man disappeared from a state hospital in Karlsruhe-Wiesloch in unexplained circumstances, the local police said.
He was convicted of the murder of one woman taxi driver and the rape and attempted murder of a second.
Authorities described him as exceptionally ready to use violence, and warned that he could be in the Bodensee area as he has contacts there.
He was sentenced to life imprisonment in February and admitted to a psychiatric institute after being convicted of stabbing a taxi driver to death in Hagenau last June. He also raped and stabbed a second taxi driver who survived, badly injured.