It happened near St Peters Church on Langton Road, Norton in Ryedale at 8am.
The pedestrian, a man in his fifties, was taken to Scarborough Hospital with a broken leg.
A Ryedale District Council spokesperson said: "A member of one of Ryedale District Council’s waste collection crews was injured on one of the rounds this morning.
"Our first thoughts are obviously with the member of staff involved, and he’s now being treated in hospital.
"Thankfully, the injuries aren’t critical, but this is obviously a serious incident.
"The police are investigating, and we’ll support them in this."