Matthew McCann was due to return to custody at Polmont Young Offenders' Institution at 4pm on Friday.
The 19-year-old was granted leave from the unit near Falkirk on December 23.
Police Scotland are asking for the public's help to trace McCann.
Inspector Billy Drummond, from the Forth Valley division, said: "Matthew McCann knew he was due to return to Polmont but chose not to.
"His failure to report back is a clear breach of the terms of his day release and anyone who can help us locate him is asked to contact police immediately.
"There is no evidence to suggest McCann poses a risk to the public. However, anyone who sees him is asked to contact police immediately."