Wilson went into the barrier after his car was hit from behind in afternoon practice at the Indianapolis Motor Speedway by compatriot Katherine Legge.
His Dreyer & Reinbold team said he had suffered a fracture of the 12th thoracic vertebrae.
"Based on this type of injury, Wilson will not be allowed to compete in this Sunday's 107th Indianapolis 500 Mile Race," the team added.
Wilson would have been starting his fifth Indianapolis 500. His brother made eight appearances but died after being hit on the helmet by debris in an IndyCar race at Pocono Raceway in 2015.
Graham Rahal (34) was later named the replacement driver for Wilson.
Rahal, who was eliminated from the race on Sunday by his own Rahal Letterman Lanigan Racing teammate Jack Harvey, will compete in his 16th Indianapolis 500.
The son of the 1986 Indy 500 champion Bobby Rahal, finished third in 2011 and 2020 and fifth in 2015.
"We have known Graham for over a decade as he drove our car in 2010 at Iowa Speedway," said Dreyer & Reinbold team owner Dennis Reinbold.
"He suffered through a tough weekend here, but we believe Graham can perform very well this Sunday."
