While he is out, Green will continue to travel with the team while working on his rehab, coach Steve Nash said.
"He has been so valuable to us this year with all the injuries we've had," Nash said Tuesday. "He's been able to play multiple positions, different roles and fill in all the gaps for us. Fortunately, we're relatively healthy elsewhere. But it is a loss."
Green, a key rotational player for the Nets this season, exited the Nets' Game 2 against the Celtics on Tuesday early with what the team called a bruised left foot. Further evaluations revealed the strain.
Celtics star Jayson Tatum also exited Game 2 after he was accidentally poked in the eye. Coach Brad Stevens said Tatum practiced on Thursday and will be ready for Game 3.
Green has started in 38 games for Brooklyn this season. At times, he filled in for injured players, and in other games, when small-ball matchups dictated it, he was a smaller, quick starting center. Green has averaged 11.0 points, 3.9 rebounds and 1.6 assists per game this season and has been a veteran voice in the locker room.
"He is a guy that has done a lot for us and means a lot to us on and off the court," Nash said. "And we just hope that he can recover fully and get back out there in these playoffs."
The Nets have struggled with injuries this season, but heading into the playoffs, they were the healthiest they've been all year. Kevin Durant and James Harden each missed over a month with a hamstring strain. Green missed a handful of games after suffering a shoulder contusion in late February. Guard Timothe Luwawu-Cabarrot also missed stretches with hip and knee issues.
Heading into Friday's Game 3, Nash said the team might be tempted to relax, given that the Nets have a 2-0 series lead on the Celtics, but added that the group understands Game 3 is a "big game."
"It's a really important game for them to stay in the series," Nash said of Boston. "So we can't take our foot off the gas. We got to not only try to win this game for this series but we also have to get better. This is our team's third game together, really -- all our rotation guys playing now, minus Jeff. So, we recognize that there is a lot at stake in this series, but also if we want to continue to improve and put ourselves in a position to be the best we can be, these games mean a lot."