After medical checks Pidcock was ruled out of the remainder of the race, which ends on Sunday.
Team doctor Lorenz Emmert said: “Due to his crash he suffered injuries, most likely bone and ligament damage in particular to his right knee and also right wrist.
“Unfortunately we had to make the decision to take him out of the race. Further clinical evaluation and imaging will follow in the next days.”
Pidcock won Milano-Torino and finished second in Milan-San Remo by world champion Tadej Pogacar this month.
“We did everything to try to make it to the start [of stage six] but it’s not possible,” said two-time Olympic cross-country mountain bike champion Pidcock.
“I fought to finish the stage yesterday to make sure I had the option to continue. Now the focus is on recovery, and I’ll be back.”
Team Visma-Lease a Bike’s Vingegaard won the stage by 51 seconds to extend his lead in the general classification to 57.