Green, who had a lengthy bat at training on Tuesday, but did not bowl like the other quicks did, did not appear at the final practice session on Wednesday.
He had bowled 22 overs at Lord's, taking on an increasingly important role after the injury to Nathan Lyon left Australia a bowler down. He played a key part in slowing Ben Stokes' scoring shortly before he was dismissed on the final day.
But Green hadn't quite been able to find his best form with the bat in the three Tests against India and England over the last month, although made handy contributions of 38 and 28 at Edgbaston.
Green, who earlier in his career suffered back stress fractures, also previously missed three Tests this year after suffering a broken finger against South Africa at the MCG.
There is a longer gap between this and the Old Trafford Test, which will give Green extra time to recover.
Marsh has a very good Test record against England: his batting average is 45.44, with both his centuries against them, and he has claimed 15 wickets at 24.46