Ritchie will remain in Scotland while the squad fly out to Japan on Monday morning but could still make the World Cup.
The Edinburgh flanker suffered a deep wound to his face during Friday’s final warm-up win over Georgia at BT Murrayfield.
The Scottish Rugby Union stated that Bradbury would travel as “precautionary injury cover”.
A statement added: “Ritchie sustained a facial injury in the national team’s 36-9 win over Georgia at BT Murrayfield on Saturday and – following specialist scans at Spire Murrayfield Hospital – will remain in Scotland for specialist assessment, with the outcome influencing whether he remains part of the 31-man group for the Rugby World Cup which begins later this month.”
Ritchie was the most serious of five injury concerns to come from the game and the other four players are set to travel.
Lock Ben Toolis and full-back Blair Kinghorn both suffered head knocks while Blade Thomson and Jonny Gray – who was making his first run out of the warm-up series – experienced hamstring issues.