The defender picked up the injury during the 3-2 win at Portsmouth in November but the problem was initially not thought to be serious.
However, a scan has now revealed Clarke suffered a hairline fracture to his foot which will rule him out until the new year.
He has been joined on the O's casualty list by striker Michael Symes, who suffered a hamstring injury after coming on as a substitute in Saturday's 2-0 victory at Bury.
Symes looks set to miss this weekend's visit of Scunthorpe as Orient attempt to make it nine successive wins.
