McGrath, sidelined from the fourth Test because of the injury, was ruled out of the two-day game against Essex at Chelmsford starting on Saturday.
He is confident, however, of being passed fit for the final Test.
England lead the Ashes series 2-1. The final Test at The Oval begins on Thursday. McGrath also missed the second Test after damaging ankle ligaments.
Essex won the toss against Australia and made a fine start, reaching 224 for one after 48 overs, with 20-year-old Alastair Cook scoring an unbeaten century. Leg spinner Stuart MacGill was hit for 56 off eight overs.
