Building work for the huge structure is about to start on fields in East Yorkshire two years after the scheme was approved, despite 1,300 objections.
Residents raised concerns over air and noise pollution, lorries parking overnight in nearby lanes and the noise of reversing HGVs late at night.
The locals say fencing going up on the field is already stopping wildlife moving around.
Campaigners want the online retail giant to incorporate the oak – referred to as T3 – into the development or dig it up and replant it in a public open space 500metres away.
The petition, with 3,671 signatures, was handed to ward councillor Margaret Corless in front of another veteran oak, T4, which was also due to be felled.
But, following pressure from locals, T4 has been placed under a watching brief.
However residents are still concerned it could be affected.
Councillor Corless said a positive response from Amazon would be an “excellent opportunity to show how it intends to work with the local community”.
She added: “I think (the development) will change the way of life for many residents permanently; it’s absolutely massive and will have a devastating impact on the village.”
A spokesman for Amazon said they were “continuing to look at all options for the site” and would comply with planning consent.
‘Learn to live alongside nature’
TV presenter Julia Bradbury suggested on X the company could make a “hole in the ceiling to allow the oak to become part of the warehouse”.
She tweeted: “We have to learn to live alongside nature, not just destroy it”.
Veteran oaks with their huge trunks support a wide diversity of wildlife.
Badgers, wood mice, butterflies and woodpeckers and jays are among the many animals that need it for food, while oaks also host hundreds of lichens, liverworts and mosses.
Jo Arro, the organiser, said: “(Amazon founder) Jeff Bezos has an Earth Fund which plants lots of trees.
“Why not save a veteran tree? If they are serious about their climate commitments they should look at relocating it. It’s been done in the UK, America and Japan.”
Residents turned out in the rain, showing the strength of feeling locally. The nearest home to the facility, which will stand up to 25metres high and operate 24/7, is just 50metres away.
One resident, Paul Sexton, said: “It’s just the loss of the greenspace and somewhere to walk. I find it incredible that there’s a national walking trail 50 yards away and they put this massive edifice here.”
Julie Bentley, who handed over the petition, said: “It’s horrendous. People who live nearby get beautiful sunsets. All you’ll see is a wall.”
Resident Duncan Ross added: “The council have totally ignored us. We pay our council tax – that’s tax without representation. They’ve ignored the whole village.”