Green sustained the injury during the final quarter of the Bombers’ win over Hawthorn on Saturday night.
“Josh Green was sprinting late in the game – he felt tight in his hamstring, came off and we didn’t end up bringing him back on,” High Performance Manager Justin Crow said.
“We’ve had the hamstring scanned and what he’s got is the lowest grade hamstring strain where the fascia around the outside of the muscle is interrupted.
“There is no real muscle fibre disruption which is a good thing but the bad news for ‘Greeny’ is he won’t be available against Brisbane.
“Normally with these injuries, players miss two games.”
Green kicked 107 goals in 81 games with the Lions, before being delisted and recruited by Essendon in November as a delisted free agent.
He collected 11 disposals and took four marks in his debut for the Bombers.