Greens Senator Peter Whish-Wilson said Mr Hunt has failed his first test on whaling as minister after years of strong rhetoric.
"If Greg Hunt has any integrity, he will resign his ministerial position," he wrote on Twitter.
Australian Sea Shepherd director Jeff Hansen said the government's specialist Southern Ocean patrol vessel, the ACV Ocean Protector, should be used for the operation - as promised before the election.
He said an aircraft will simply fly in and out in a matter of minutes and customs officers will be unable to make arrests.
"It's really going to have no impact whatsoever. It's a waste of taxpayer dollars," he said.
Both Sea Shepherd and the Greens said the move is a broken election promise.
In the lead-up to the September election Mr Hunt did pledge that a Customs vessel would monitor the whale hunt.
Sea Shepherd Australia chairman Bob Brown said the government backdown is ugly and irresponsible.
"They are effectively turning a blind eye to the Japanese slaughter," he said.
But Mr Hunt said on Sunday that using an aircraft provides greater range, flexibility and speed instead of relying on a ship.
It's also believed that the specialist patrol vessel is now preoccupied with patrolling waters off Christmas Island for asylum seeker boats.
Japan's whaling fleet is expected to arrive in its planned hunting zone in the Southern Ocean before the end of the year.
The chosen customs aeroplane, currently contracted to the Australian Antarctic Division, will make regular flights, likely in and out of Hobart, for the entire whaling season, from January to March 2014.
Australia took legal action in the International Court of Justice after decades of diplomatic efforts failed to curb Japan's whaling program.
A ruling has not yet been made, though Mr Hunt said he's hopeful an announcement could come soon.
- AAP
