Siriyakorn Siriboon, nicknamed Bung, vanished during a 10-minute walk to school, Detective Inspector John Potter from the homicide squad said.
The last person to see her was a neighbour who watched her begin the walk to Boronia Heights College, in Melbourne's eastern suburbs, on June 2.
Det Insp Potter said there was a possibility the teenager had died and the homicide squad had taken a more active role in the investigation in the past week.
Despite the fears, Det Insp Potter said Bung's family still believed she was alive.
He said the girl may also have been abducted, but he discounted early speculation that Bung led a double life using social media websites.
"We don't believe her use of social media is connected to this case," Det Insp Potter said.
"This is a worrying case, worrying because here is a girl 13 years of age walking to school who disappears.
"We have had nothing, no information to suggest what has happened to her."
Asked whether there could be links to the Mr Cruel attacks on young girls in the late 1980s and early '90s in Melbourne's eastern suburbs, he said no connection with other disappearances had been drawn.
Child rapist Mr Cruel was believed to be responsible for at least four attacks on children, and two of his victims were 13-year-old girls.
While three of the victims were released, Mr Cruel went on to murder his last known victim, 13-year-old Karmein Chan.
Mr Cruel was never caught but police last year said a fresh taskforce had been established to track him down.