Witnesses said the man was run over by the council-branded vehicle while lying on the ground in the BBQ area of London Fields, Hackney.
A Hackney Council spokesperson said the driver - "an agency member of staff" - was picking up rubbish in the park when the "serious incident" occurred. The injured man was lying on an area of short grass.
The man - who is believed to have a fractured cheekbone - was taken to hospital by air ambulance.
"Our thoughts are with them and their family. This is obviously a serious incident and both the police and ourselves are investigating," the spokesperson said.
London Fields is a popular site for BBQers but has led to repeated complaints from locals about the vast amounts of litter left behind on sunny weekends.