Building an underground pipeline through the New Forest National Park would involve a construction corridor the width of an eight-lane motorway, campaigners say.
The massive project would cause "irreversible damage" to the environment, according to an online petition that has already been signed by more than 1,400 people.
The petition also claims the scheme would harm marine life as well as posing a potential risk to human health.
If the scheme goes ahead, millions of tonnes of the greenhouse gas will be dumped underground instead of being released into the atmosphere.
Three possible routes for the pipeline have been put forward, including two on the western side of the Isle of Wight.
One route would cut through the New Forest, diving under the Solent between Milford and Barton. The other two would run south from Fawley, passing under the seabed before crossing the Island.
The scheme has come under fire at public consultation events in the Forest, where construction corridors 50m wide will be created if the mainland route is chosen.
ExxonMobil has said an Isle of Wight route is preferred.
But the company has told Fawley Parish Council that the Island is no longer an option for various technical reasons, according to a member of New Forest District Council.
Cllr Allan Glass said the New Forest now appeared to be the favoured route.
Launched by Forest resident Ines Graham, the petition says: "Carbon capture is an international priority and must be addressed urgently. However, this should not be at the expense of environmental destruction.
"The pipeline would cut through protected natural areas and disrupt ecosystems and habitats.
"The construction process, requiring a space equivalent to an eight-lane motorway, would destroy natural vegetation and cause significant land and soil disturbance by compaction and root disturbance, which in turn would impact crops and natural habitats.
"The contemplated corridors include designated sites with the highest national and/or international protection."
The petition also says any CO2 leaks could harm human health.
"In Mississippi a serious leak resulted in unconsciousness, evacuation, and 49 hospitalisations. In Louisiana there was a leak of an estimated 2,548 barrels, with a significantly delayed emergency response."
An ExxonMobil spokesperson said: "Currently two corridors on the Isle of Wight are favoured, but the mainland corridor is still being considered.
"The Lepe corridor, south of Fawley, is included in all three options. Our consultation aims to gather feedback to help us decide and we will share updates once a route is selected."
The company has not responded to concerns raised in the petition.
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