Sutton was taken to hospital after suffering bruising and bleeding on the brain in a bike accident on Thursday, a day after British Olympic time trial champion Wiggins was also involved in a smash on an English road.
Wiggins was discharged from hospital on Thursday.
"Bradley Wiggins is continuing to make good progress following his road traffic accident on Wednesday evening," his Sky team said in a statement.
"Following further examination Team Sky's medical staff can confirm that as well as bruising he also has a fractured rib, a bruised lung and a dislocated finger. These injuries are being monitored and he will make a full and speedy recovery."
Wiggins, known for his outspoken rants, spoke of his gratitude to those who had helped him since his accident and said sorry for sticking his finger up at photographers as he arrived home.
"Although I'm still a little bit sore I will now be spending time at home with my family and concentrating on making a full recovery," he said.
"I would also like to apologise for the gesture that I made when I arrived home yesterday afternoon. I was tired, in a lot of pain and just wanted to get inside, but I shouldn't have reacted the way I did. I'm sorry for that.
"I'm looking forward to getting back on the bike soon and continuing my preparations for the 2013 season."
The woman who allegedly knocked Wiggins off his bike in her van has been summonsed by police over driving without due care and attention, media reports said.
Sutton was also knocked off his bike and his condition is improving too.
"Shane is making steady progress but is likely to remain in hospital for one more day under observation," a spokesperson for British Cycling said.
"He has fractured his cheekbone which will require surgery in due course. He is expected to make a complete recovery and will be back in work shortly."