Green was hurt during the last one-day international against South Africa in Potchefstroom on Wednesday after being struck in the stomach by a full toss from Corbin Bosch that left him writhing in pain. Two balls later, his attempted pull shot bounced off his gloves, and he was not only caught but strained his muscles as he fell to the ground.
"It's an odd one and had our medical team scrambling, so I'm not going to go down what the medical said around it, but there's not a hell of a lot of evidence in these injuries in cricket," McDonald told a press conference.
"They said it's a stabilising muscle, so I think that's a better result than a rotational muscle."
Green remains in contention for the second Test in Gqeberha and the third in Cape Town.
"He's progressing pretty well, all things considered, on the back of the injury that he had to his abdominal," McDonald said.
"He's still here for a reason, so there is some light at the end of the tunnel. It'll just be a matter of going through the rehab.
"It's a bit of an unknown, but there's still optimism that he'll take part in the series at some stage," the coach added.
The 27-year-old started the tour of southern Africa with a sore shoulder which kept him out of the three ODIs against Zimbabwe, but he did play in the three ODIs versus South Africa.
Green's absence will be a blow as he is considered one of the form players in the touring party, especially after he scored a first home Test century when Australia suffered a shock loss to Bangladesh in Darwin in August.
Cooper Connolly, 23, could be in line for a second Test appearance after his February debut in Galle against Sri Lanka as Green's replacement, although Australia will not be settling on their line-up until they better assess the pitch conditions, McDonald added.
