The company wanted to build a large depot on Erith Marshes in Bexley. The area's high ecological significance is recognised by the Greater London Authority, the Environment Agency and the Bexley biodiversity action plan.
The marshes are on the Thames flood plain and the Environment Agency is investigating their potential as a flood storage area.
An Asda spokesman said the application has been withdrawn because it was on a greenfield site. The supermarket has now submitted an application to the London Borough of Bexley for a depot on a brownfield site, which will involve refurbishing an existing building.
The Green Party welcomed Asda's decision. MEP Jean Lambert has been calling for the protection of the grazing land for almost four years. She insisted that it is completely wrong for the site to be developed when there are more suitable local sites.