Cummins confirmed Green will continue at number five in Australia's XI in the series opener starting in Darwin on Thursday, despite struggling for runs during the Ashes.
"We like it when he's nice and busy and putting pressure back on the bowlers, he's really intimidating," Cummins told reporters in Darwin on Wednesday.
"Same with when he's bowling, having that presence.
"He's quite an intimidating sight when he gets going. You see him in some T20 games, he's beating the ball around."
Green averaged 24.42 with the bat in the Ashes but is batting higher than fellow seam-bowling all-rounder Beau Webster, who has barely put a foot wrong in his eight tests.
Batting at number nine, Webster scored an unbeaten 71 at the Sydney Cricket Ground in the fifth test against England and is averaging 41.09 with the bat.
He will bat at number seven, with wicketkeeper Alex Carey at six.
Some Australian cricket pundits have grown impatient with Green's progress and questioned his place in the team, but Cummins said there was no pressure from his teammates.
"He's almost got too many skills, so it's like 'just get out there, assert yourself, strip it away, there’s no pressure from us,'" said the skipper.
"Just go, you’ve got freedom, get out of your own way and just go play.'"
The Darwin test sees Australia's elite pace attack of Cummins, Mitchell Starc and Josh Hazlewood teaming up with long-serving spinner Nathan Lyon for the first time in more than a year.
Hazlewood, who missed the Ashes due to Achilles and hamstring problems, edges out fellow quick Scott Boland.
Cummins said it was a tight call between Hazlewood, who has 295 test wickets and an average of 24.21, and Boland, who was a standout against England.
"(Boland) knows his worth and how good he is, I’m sure he’ll be out there at some point pretty soon," added Cummins.