All-rounder Ali is nursing a side strain, while fast bowler Finn injured his left knee while batting in training on Thursday.
The pair will miss England's opening match against a Western Australia XI at the WACA in Perth, starting on Saturday, and the four-day match against a Cricket Australia XI in Adelaide starting on November 8.
"Finn will be monitored by the England medical department over the next seven days and a further decision on his fitness will be made at that time," the ECB said in a statement.
"Ali has aggravated his left side. He is expected to return to full training by mid-November ahead of the tour match in Townsville, starting on Wednesday November 15."
England begin their attempt to retain the Ashes in the first Test in Brisbane on November 23.