Hazel North, 19, from Dunfermline in Fife, was last in contact with her family almost three weeks ago.
The arrest of a 25-year-old man follows the discovery of a woman's body in a park 60 miles away in Kilmarnock, East Ayrshire, earlier today.
Ms North had told her sister on March 4 that she was travelling to the town to meet a friend.
A Police Scotland spokeswoman said: "We can confirm that a 25-year-old man has been arrested and is presently detained in police custody in connection with her death. A report will be submitted to the procurator fiscal."
The suspect is expected to appear at Kilmarnock Sheriff Court tomorrow.
Police said earlier that they believe the human remains found in Dean Park are those of Ms North, who lived in Dunfermline's Cairneyhill area.
A post-mortem examination will be carried out tomorrow.