His injuries, which also include a minor lung contusion, were sustained when his Emil Frey Lamborghini Huracan GT3 Evo was involved in a multi-car incident in the opening hour of the double-points round of the GT World Challenge Europe.
The fractured vertebra was described as stable and Aitken is hoping to be discharged from hospital in Liege either today or tomorrow in order to return to the UK to continue his recovery.
Aitken, who was sharing the Emil Frey Lambo with Arthur Rogier and Konsta Lappalainen, said in a statement: “All things considered I feel fine, and quite lucky.
“I’m also sorry for my teammates that we didn’t get to compete, and for the other cars involved.
“The aim now is to get back to the UK and start to recover as best as possible and be back in the car soon: I’m sure with the people around me I’ll manage it just fine!”
The British-Korean driver, who is undertaking both the Endurance Cup and Sprint Cup legs of the GTWE this year, also thanked the marshals and medical staff at both the track and the hospital.
No timeline has been set for Aitken’s return to the cockpit of a Lamborghini or when be able to fulfil his F1 role with Williams.
The next GTWCE round is scheduled for Brands Hatch on the last weekend of August.
Ferrari factory driver Davide Rigon, who was also taken to Liege hospital, was released before midnight after a check-up.
The Italian, who was racing an Iron Lynx Ferrari 488 GT3 Evo, was discharged wearing a back brace as a precautionary measure.
A Ferrari spokesman said that it was too early to say whether Rigon will be able to take up his seat for the Le Mans 24 Hours World Endurance Championship round later this month.
He explained that a decision will be made on the coming days on whether he will drive the #52 AF Corse-run factory 488 GTE Evo together with Miguel Molina and Daniel Serra after further assessment of his condition.
Kevin Estre and Franck Perera were the other two drivers involved in the incident respectively driving a Rutronik Porsche and an Emil Frey Lamborghini.
They were both given the all-clear after check-ups at the circuit medical centre.
The accident happened less than 30 minutes into the race.
No official TV coverage of the incident or its aftermath has been released, but Aitken appears to have lost the car at the second left of the Eau Rouge/Raidillon sequence.
He was then collected by Emil Frey team-mate Franck Perera and Estre.
The incident resulted in a yellow-flag neutralisation of the race lasting more than hour.
The race was led shortly before the 18-hour mark by the second of the factory-backed Iron Lynx Ferraris, which is shared by Alessandro Pier Guidi, Nicklas Nielsen and Come Ledogar.