Alex Ritchie, 52, the engineer on Mr Branson's current round-the-world attempt, suffered multiple injuries in the accident in Morocco but is not thought to have suffered spinal injuries.
Mr Branson said he was "very shocked" at the news but said his round- the-world balloon attempt would go ahead as planned.
Mr Ritchie, who is married with two children, was making the sky dive with the third member of the team, Per Lindstrand.
"He was using a hand-deployed parachute which did not deploy and it was only quite close to the ground that he managed to get it partially opened," Mr Branson said.
"Although he is seriously injured he is believed to be stable and his injuries are not thought to be life threatening.Reuse content