Green, 26, has played for Mumbai Indians and Royal Challengers Bengaluru in the IPL, scoring 707 runs at a strike-rate above 150 and taking 16 wickets in 29 games.
Although he was sold in the capped batters category, Green said he will be available as an all-rounder and attributed the listing to a "stuff-up" by his management.
Green has struggled with back injuries throughout his career and missed the 2025 IPL following surgery.
He returned to action as a specialist batter in June but is being used an all-rounder by Australia in the ongoing Ashes series against England.
The IPL auction is ongoing, with 18 England players on the longlist.
Opener Ben Duckett will make his IPL debut after being picked up by Delhi Capitals for 2 cr (£167,000) but Liam Livingstone, Gus Atkinson, Jonny Bairstow, and Jamie Smith went unsold.