The Swiss man admitted to killing the 25-year-old Pole in a Zurich hotel last week before bringing her body back to his flat, where he was confronted and arrested by police on Wednesday, reports news agency ATS.
The victim, a Polish woman who was working as a dancer in a Zurich nightclub, had been due to return to Poland last week, cantonal police said in a statement on Thursday.
When she failed to arrive, she was reported missing to the Polish authorities, who asked Zurich police for help in finding her.
Officers traced the man to his apartment thanks to the guest registration form of a Zurich hotel where the man and his victim spent the night of September 15th, shortly before she disappeared.
The circumstances surrounding the murder are not yet know.
This is the second murder case in Switzerland in the past week after the body of a 36-year-old Bulgarian prostitute was found in Lake Lucerne on Sunday.
Police in Basel are investigating the death of another woman whose body was pulled out of the Rhine near Basel on Wednesday afternoon.