The man allegedly followed her out onto the street and raped her on an empty beach.
Local media report that the woman was covered in injuries from sticks and stones on the beach.
The man has pleaded not guilty to the charges.
DNA samples have been collected for comparison.
According to MailOnline, the victim is currently "in a state of disbelief", allegedly telling police her father could not have been the man who raped her.
Police will keep the father in detention until at least Tuesday, which is the deadline for him to issue a public apology for the crime. Greek law allows for reduced sentences for people who admit their guilt and apologise before sentencing. The provision is available to those accused of rape.
SEXUAL HARM - DO YOU NEED HELP?
If it's an emergency and you feel that you or someone else is at risk, call 111.
If you've ever experienced sexual assault or abuse and need to talk to someone contact the Safe to Talk confidential crisis helpline on:
• Text 4334 and they will respond
• Email support@safetotalk.nz
• Visit https://safetotalk.nz/contact-us/ for an online chat
Alternatively contact your local police station - click here for a list.
If you have been abused, remember it's not your fault.