The British rider fell from his bike after colliding with Simon Gerrans of the Orica-GreenEDGE team during a sprint finish for the line at the end of Stage 1 of the Tour in Harrogate, Yorkshire.
The 29-year-old also suffered ligament damage in the fall, but he accepted the fault lay with himself, as the BBC Sport article noted.
Cavendish is quoted as saying:
It was my fault, I'll apologise to Simon.
I tried to find a gap that was not there. I wanted to win.
Cavendish, who rides for Omega Pharma-Quick-Step, was considered to be among the favourites to win the Green points jersey at the Tour this year, and he is third in the all-time list of most Stage wins with 25.
British hopes for a third successive Tour winner lie with Chris Froome, who succeeded Sir Bradley Wiggins as the race champion last year.
Cavendish knew the injury was serious immediately, reports BBC Sport.
The 'Manx Missile' is quoted as saying:
I'm absolutely devastated.
I had some optimism that the swelling would go down overnight, but it's worse this morning.
I knew straight away because normally in crashes I bounce back straight away.
This was the first time in my career that I knew something was up, but I wanted to finish. I was able to do that, but I was in pain.
Cavendish was one of four British riders in Le Tour, alongside Froome and Geraint Thomas of Team Sky, and Simon Yates of Orica-GreenEdge.
The injury now places a doubt over Cavendish's participation in the Commonwealth Games later this month.
Missing out on the Glasgow Games will be a major blow for the Manxman, who would have been representing the Isle of Man.
Cavendish became the first Manx athlete for 20 years to win a gold medal at the Commonwealth Games, when he crossed the line first in the 20km scratch race in Melbourne, Australia, in 2006.
But he missed out on a potential gold medal at the London 2012 Olympics when he finished a disappointing 29th in the race.