The 28-year-old sustained the injury during training on Thursday and will now return to the UK and meet with specialists to determine whether surgery will be required on the problem.
Scans showed that Finn, who was added to the squad following Ben Stokes's arrest, tore the cartilage in his left knee, forcing him to miss the entirety of England's tour Down Under.
"Steven Finn will miss the remainder of England's tour of Australia after scans revealed that he has torn a left knee cartilage," read a statement on the ECB's website.
"The Middlesex seamer sustained the injury during practice last week in Perth and will now return to the UK in the next 48 hours where he will meet a knee specialist to ascertain whether he will have an operation.
"England will announce his replacement for the rest of the tour in due course."
England's first warm-up match against a Cricket Australia XI begins on Wednesday, while the first Test gets underway in Brisbane on November 23.