The Australian, 32, who drives for the Red Bull racing team, was airlifted to hospital where he underwent surgery on a broken right leg.
"The surgery is complete, a pin inserted and the recovery begins," said the event's director, Geoff Donohue.
The accident happened south-east of state capital Hobart on Saturday.
Webber was taking part in the Mark Webber Pure Tasmania Challenge, a 250km endurance event consisting of mountain bike riding, kayaking and trekking on the Australian island.
He was riding a bicycle along a road near historic Port Arthur when he collided with a four-wheel drive vehicle at 1240 local time.
"Mark's in good spirits," said Donohue. "The broken leg is the injury, and beyond that, he's in really good shape.
"He has a little bit of a graze on his left forearm, but he has had full scans and everything else is clear.
"He'll be in hospital for at least three days, for sure under a week. I was speaking to him before the operation, and he was already thinking about his rehabilitation."
Sergeant Jon Ford, of Tasmania Police, said: "We received reports of a collision between a bicycle and a motor vehicle on the Fortescue Bay Road on the Tasman Peninsula.
"He was airlifted from the scene by helicopter and taken to the Royal Hobart Hospital where he is now being treated for serious but not life-threatening injuries.
"He suffered a broken leg and other injuries and is reported to be in a stable condition."
Webber, who is also a BBC Sport columnist, finished 11th in the Formula One drivers' world championship standings this year.
Red Bull have already begun testing ahead of the 2009 F1 season. The team's next testing session is scheduled to take place in Jerez, in southern Spain, from 9 December.
"That date obviously will be an issue," said Donohue.
"But I suspect that as soon as Mark is able to fly, they will be keen to get him back to Europe.
"They will have people working out his rehab program now with a view to getting him up and going as soon as possible."