Libbi Toledo, 17, was last seen in Kirkcaldy on Monday afternoon.
The body of a female was later discovered at the scrapyard at the the junction of the town’s Denburn and Smeaton Roads, around 2pm this afternoon.
Police told the BBC that the death of the woman was being treated as unexplained as inquiries continue.
A cordon is still in place in the area.
A press conference was due to take place this afternoon with the mother of Libby, but it was cancelled at short notice due to what the force described as a “significant development.”
Libbi was last seen in the Veronica Crescent in the Smeaton area of the Fife town at around 1pm on 11 September. She was spoken to at around 6pm that day and said she was at a friend’s house, believed to be in the local area.
However, when she failed to return, the alarm was raised at 1.45am the following morning.
Police Scotland had said they are “very concerned” about the 17-year-old’s welfare that it was unusual for her not to make contact with family and friends.
The police search yesterday had focused on Denburn Road close to the town’s Victoria Hospital, less than a mile away from where Libbi was last seen. A police cordon was in place in the area north of the town centre, which features several industrial units, including a former scrap merchants.
On Wednesday, Judith appealed for her daughter - who has ADHD and suffers from mental health issues - to come home.
She said: “Just come home. You’re not in any trouble, just come back and get the support you need, and be with your mum. Just let me know you’re okay.
“I don’t care about anything that’s happened in the last week, just come home.”
She added: “Someone has to know where she is. She’s very, very easily-led and impressionable. She’s a very high-risk individual.
“Even if it’s as innocent as someone saying ‘don’t worry, you’re over 16, you don’t have to go back’.
“Somebody’s either got her, or hiding her, thinking they’re protecting her but that kind of thing’s only going to do more harm than good.”
There have since been six reported sightings of Libbi, who is 5ft 7in, with brown eyes, pierced ears and was last seen with dark blonde hair. She was wearing a black sleeveless shirt with white logos over the front, a purple crop top underneath and black military-style boots.
Three of the sightings were found not to be her. Inquiries are continuing into the other reports.
The first was outside Morrisons supermarket on the Esplanade in Kirkcaldy. She was in the company of a young man of a similar age, 5ft 8ins, clean-shaven and thin, wearing a black hoodie with the hood up, at about 2pm on 11 September.
The second was a possible sighting of Libbi with a group of around seven males and three females in Alison Street between 12 and 1pm on 13 September.
The third was a potential sighting of her in Alison Street at around 7.45pm on last Friday with a man described as being in his late 20s or early 30s, with a blond mohawk haircut.