The four-car incident occurred during the opening hour of Saturday’s 24-hour race at the top of Eau Rouge, one of the fastest points of the Spa-Francorchamps circuit.
Aitken and Rigon have both been transferred to hospital with “no life-threatening injuries”, according to a statement issued by the event organisers.
Porsche factory driver Kevin Estre and Franck Perera were also involved in the crash but have been discharged from the circuit's medical central following precautionary checks.
The race has since got back underway after more than an hour running under a Full Course Yellow and Virtual Safety Car while barrier repair work was carried out.
Aitken made his F1 debut with Williams at last year’s Sakhir Grand Prix when George Russell was called up to replace Mercedes’ Lewis Hamilton after the seven-time world champion contracted COVID-19.
The Briton has been dovetailing a sportscar programme in the GT World Challenge series alongside some Formula 2 outings this year.
“Sending our best wishes to our reserve driver Jack Aitken following an accident at the 24 Hours of Spa,” Williams said in a statement on social media.
“Jack has been taken to hospital for further evaluation and fortunately with no life threatening injuries. Everyone at the team wishes him a speedy recovery.”
Sending our best wishes to our Reserve Driver Jack Aitken following an accident at the @24HoursofSpa.— Williams Racing (@WilliamsRacing) July 31, 2021
Jack has been taken to hospital for further evaluation and fortunately with no life threatening injuries. Everyone at the team wishes him a speedy recovery. pic.twitter.com/1XaKy0TQE4