The 32-year-old former Australia A player will continue his recovery at a private hospital in Bristol once he has returned from France in an Air Ambulance.
"Marc has had an operation to stabilise his neck following damage to a disc and a crack in a bone," said Dragons chief executive Gethin Jenkins.
"The operation has gone well and he has movement in his arms and legs.
"Our main priority is his long-term wellbeing and we are grateful to the hospital staff, along with those at the Toulouse club, for their professionalism and support.
"Marc is in good spirits and we hope to have him back in Wales as soon as possible."
Despite the seriousness of his injury, Stcherbina, who has also worn the colours of Northampton Saints and Cardiff Blues during his time in the UK, has already passed on his support to his team-mates ahead of their return fixture with the French giants at Rodney Parade this Saturday.
He will return home wearing a support for his head, neck and chest, and the Dragons have confirmed that regaining his health rather than his rugby career will be the Australian's immediate priority.
"Marc is concentrating on returning to full health in everyday life, not thinking about his rugby future," added the Dragons' rugby manager Rob Beale.
"Playing rugby will be the furthest thing from Marc's mind at the moment, all he wants to do is get home and get back on the road to recovery.
"His rugby future is a decision for Marc, his family and the doctors."