Annalise Johnstone’s body was discovered by a member of the public on a country road near Auchterarder two weeks ago.
Police are now treating the case as murder.
The Senior Investigating Officer, Detective Superintendent James Smith of the Major Investigation Team said : “I can confirm today that we have arrested a 24 year old man in connection with the death of Annalise, which is now being treated as murder.
“Our thoughts are very much with Annalise’s family and friends, who are still being supported by specialist officers during this difficult time.’
“A number of enquiries are being carried out at locations across Tayside as part of our investigations into her death.
“Enquiries have necessitated the closure of the B8062 and I am grateful for the patience of local residents and motorists while this work is being carried out.
“I would also like to take this opportunity to thank members of the public for their assistance during this investigation”.