Race leader Taylor Phinney was also involved in the mass pile-up near the end of the stage in the Danish town of Horsens, which was won by Australian Matt Goss.
The crash occurred when Italian rider Roberto Ferrari cut abruptly across Cavendish's line within 100 metres of the finish. Cavendish could not avoid the Italian and tumbled violently to the ground, lying prostrate on the tarmac as another rider rode over him.
Cavendish sustained a bad cut on his left shoulder, but Team Sky spokesman confirmed that he will continue in the race. American Phinney hurt his ankle, but will also continue.
The 26-year-old Cavendish took to Twitter to vent his rage at Ferrari.
"Crashing at 75kph isn't nice! Nor is seeing Roberto Ferrari's manoeuvre," said the Team Sky rider, before calling on Ferrari to be thrown out of the race.
"Is the team of Roberto Ferrari or the UCI going to do the right thing? Other riders, including myself, have been sent home for much less."
Ferrari himself remained unmoved, saying, "I was doing my sprint, I have nothing to say," though his team manager apologised on his behalf.
Phinney received medical assistance from an ambulance before hobbling towards the race podium with a huge bandage around his ankle to receive his leader's jersey.
"First of all I want to reassure my family I'm fine, but it was a bad cut," Phinney said. "I was in a state of shock when I got in the ambulance, I'm glad it's a rest day tomorrow. It's a shame when things like this happen."
BMC Racing team doctor Dario Spinelli added: "It's definitely good that this happened before a rest day, since the transport and treatment process took so long. Taylor will enjoy a good night of sleep without the stress of having to get ready to race."
Cavendish then walked towards the line, his shoulder visibly cut and his red jersey of points leader in tatters.
"He lost a lot of skin but he is okay," Team Sky sports director Steve De Jongh said.
"It looks like there's nothing broken. It was a really nasty crash, I think the guy who caused that should be punished. You cannot make a manoeuvre like that."
Ferrari blamed another rider for his abrupt manoeuvre and said he had not seen Cavendish.
Told that he had been relegated to the last place in the pack by the race officials, Ferrari replied: "I've nothing to say about that, I was doing my sprint."
The stage began with a memorial ceremony for Belgian rider Wouter Weylandt, who died in an accident on stage three of the Giro last year, and for Horsens mayor Jan Trojberg, who died suddenly on Sunday.
Tuesday is the first rest day as the race moves to Italy. Racing resumes with a team time trial on Wednesday in Verona.