England coach Ashley Giles confirmed the decision on Wednesday after arriving in Brisbane for Friday's second one-day international in Brisbane.
Giles says Finn needs to take a break and will benefit more from heading home now than continuing on in the tour.
The Middlesex quick didn't feature in any of the five Tests of the recently completed Ashes after failing to impress in warm-up tour matches.
"We feel it's the best thing for him," Giles said.
"We feel he's not been bowling that well and not bowling well enough to get selected. I feel the best place for him to be right now is out of a performance environment."
The news continues a horrible tour for England after Jonathan Trott and Graeme Swann both went home during the Test series, won 5-0 by Australia.
Despite the decision to send Finn home, Giles is confident the tourists can win at the Gabba on Friday to level the five game series 1-1.
"This is going to be a tough series, we're one-nil down, our focus has to be on trying to win this series," he said.