The nine 30-year-old trees on Ashley Road were cut down earlier this month. The council intends to replace them with other varieties.
Cabinet member for highways Terry Douris said: "This is a virulent pest and unless it's dealt with it could infect more sweet chestnut trees and pose health and safety problems for residents."
The step was taken after the council was served with a Statutory Plant Health Notice by the Forestry Commission because OCGW is a quarantine pest.
Ashley Road is the second UK site where the wasp has been detected. The first was at Farningham Woods near Swanley in Kent, where the pest was found last month. The trees were coppiced.
Restricted to Castanea trees, the wasp's larvae cause green or rose-coloured galls on leaves, petioles and twigs, weakening the tree and making it more susceptible to other pests and diseases, such as sweet chestnut blight.
No other organism is known to cause galls on sweet chestnut trees so their presence is a reliable indicator of OCGW infestation. Suspected sightings should be reported to email@example.com.