"Absolute arsehole of a day, but nothing that will stop me getting amongst it tomorrow," tweeted the 29-year-old after his double fall.
The Jumbo-Visma team rider first came a cropper around 100km from the end of the 18th stage after a collision with Ireland's Nicolas Roche.
He dusted himself off, got back on the bike but was reacquainting himself with the asphalt again on the final descent.
"Our medical staff have taken care of @georgenbennett's wounds," the team tweeted.
"A first check didn't point out major injuries. Later today our medical staff will conduct additional research."
Bennett finished the day in 27th place, 11 minutes behind stage winner Nairo Quintana.