Sutton was involved in a crash on the A6 near Levenshulme in Manchester, and is likely to be in hospital for several days.
"Shane was taken into hospital where it was identified he has suffered bruising and bleeding on the brain," a British Cycling statement said.
"Shane was wearing a helmet. He is set to undergo more tests, and is likely to stay in hospital for the next few days."
The accident happened just a day after British cycling superstar Bradley Wiggins was knocked off his bike during a training ride, and British Cycling's statement called for more to be done to improve conditions on the road for cyclists.
"It is extremely rare that our riders and coaches are hurt while out cycling on the road, even rarer that two incidents should occur in a short space of time, and we wish Shane and Bradley a speedy recovery.
"Cycling is not an intrinsically dangerous activity but there is much more to be done to improve conditions for cyclists on the roads.
"British Cycling is calling on the government to put cycling at the heart of transport policy to ensure that cycle safety is built into the design of all new roads, junctions and transport projects, rather than being an afterthought."