Rossi crashed at turn eight during the opening practice session in Canada and was captured cradling his thumb after the incident.
The McLaren driver missed the race and was replaced by Frenchman Theo Pourchaire.
Rossi will return for the upcoming Gateway race on August 18.
“Alexander Rossi has been cleared by the IndyCar medical team to race next weekend’s event at World Wide Technology Raceway,” a statement read in part.
“Following an incident in Practice 1 during the Indy Toronto Grand Prix, Alexander was unable to compete.
“Theo Pourchaire was brought in to fill the seat, while Alexander focused on his recovery back in Indianapolis.
“This week, Alexander was cleared and is set to race his No. 7 VELO Arrow McLaren Chevrolet for the remainder of the 2024 season.”
Rossi is set to depart McLaren at the end of the 2024 season.
He will be replaced by Christian Lundgaard who will join Pato O’Ward and Nolan Siegel at the team.