The 29-year-old was taken immediately to hospital after falling 250m from the finish line in Harrogate following a collision with Australian rider Simon Gerrans.
Cavendish will decide tomorrow whether or not he will continue his participation in the event.
"I'm gutted about the crash today," the Omega Pharma-Quick Step rider said in a team statement. "It was my fault. I will personally apologise to Simon Gerrans as soon as I get the chance.
"In reality, I tried to find a gap that wasn't really there. I wanted to win today, I felt really strong and was in a great position to contest the sprint thanks to the unbelievable efforts of my team. Sorry to all the fans that came out to support. It was truly incredible."
The statement continued: "Mark Cavendish underwent further examination on his right shoulder after today's crash. The imaging underlined ligament ruptures, with an AC-joint dislocation, which causes him a lot of pain. A final decision on his participation in tomorrow's stage will be taken tomorrow morning."
The Tour de France continues tomorrow with a 201km race from York to Sheffield.