The Middlesex quick joins Toby Roland-Jones, Mark Wood and the currently suspended Ben Stokes as seam bowlers who are unavailable to the tourists.
Finn has been replaced by Surrey's Tom Curran, who has yet to play a Test Match, but has impressed during his fledgling international career.
Finn ruled out after suffering training injury
The unfortunate Finn, who was deemed 'unselectable' during the last tour to Australia, was bending down to pick up a ball last Thursday before suffering the freak injury.
He will now return to the UK to decide whether surgery is needed to cure the issue which has curtailed his participation down under this winter.
In his place, the 22-year-old Curran will jet out to Australia to join a fast-bowling battery that looks decidedly short of experience behind the duo of Jimmy Anderson and Stuart Broad.
Crane given opportunity in day/night warm-up fixture
Curran will battle with the likes of Craig Overton and Jake Ball for selection, with those two named in the England XI for their warm-up match at the Adelaide Oval which begins on Wednesday.
Anderson, Overton and Ball are joined in the bowling department for the fixture by Chris Woakes and young leg-spinner Mason Crane who may have to debut during this Ashes series if Moeen Ali's side injury does not clear up.
Alastair Cook will open up alongside Mark Stoneman, with the Yorkshire duo of skipper Joe Root and Jonny Bairstow joining James Vince and Dawid Malan in the top six.
Starc hitting top form during Sheffield Shield
In worrying news for the tourists, Australia's premier strike bowler Mitchell Starc seems to be hitting his straps at the perfect time.
The left-armer made history by taking two hat-tricks in the same first-class match during New South Wales' 171-run win over Western Australia.
The two hat-tricks accounted for six of Starc's seven dismissals during the four-day contest, and they may have been wickets 8, 9 and 10 in each innings, but his ability to produce unplayable yorkers against the England tail is likely to be a huge factor in the upcoming series.