In his absence, star batter Steve Smith will be donning the captaincy armband for the first Test at Perth, with Cummins now aiming to be fit for the second Test in Brisbane from December 4.
Cummins, who was previously optimistic of taking part in a significant chunk of the series, appears to have no chance of playing the series opener in Perth from November 21 and could even miss all five Tests, leaving superstar batter Steve Smith as his stand-in captain.
Green, who is not a part of the ongoing T20Is against New Zealand, will be playing at fourth spot for Western Australia in his first Sheffield Shield outing in 18 months. He expects a return to the number three spot when the first Ashes Test is played at Perth on November 21.
The English bowler has taken three wickets in the ongoing second Test match of the Ashes series against Australia on Thursday at Lord's. He had also taken five wickets in the first Ashes Test.
Most Australian players would like some days of rest before the second Ashes Test but that may not be the case with two of the side's most consistent batters. Australia won the first Ashes Test without much contribution from this prolific pair as they could score only 35 runs among them.
England head coach Brendon McCullum feels the first Ashes Test "validated" his team's aggressive strategy and expects his side to "go a little harder" in the second Test at Lord's next week.
Andy Pycroft of the ICC Elite Panel of Match Referees imposed the sanctions after the teams were ruled to be two overs short of their targets after time allowances were taken into consideration.
Partnership between Usman Khawaja and all-rounder Cameron Green kept Australia's hopes alive after the end of the afternoon session on the last day of the first Ashes Test against England at Birmingham on Tuesday