Walker, who was an early pacesetter for Pr1mo Bournemouth Kawasaki, crashed halfway through the session at Clarks to bring out the red flags. He is being assessed at the medical centre.
If the fractures are confirmed it is likely he would be ruled out for the remainder of the season.
Rapid Solicitors Kawasaki rider Byrne emerged fastest on a drying track in Scotland ahead of Swan Yamaha’s Tommy Hill and Samsung Honda’s Michael Laverty.
WFR Honda's James Westmoreland also crashed out early, but was unhurt.
1. Shane Byrne (Rapid Solicitors Kawasaki) 49.510s
2. Tommy Hill (Swan Yamaha) +0.179s
3. Michael Laverty (Samsung Honda) +0.295s
4. Josh Brookes (Tyco Suzuki) +0.403s
5. Tristan Palmer (GBmoto Honda) +0.508s
6. Alastair Seeley (Tyco Suzuki) +0.575s
7. Luca Scassa (Padgetts Honda) +0.612s
8. Alex Lowes (WFR Honda) +0.756s
9. Tommy Bridewell (Supersonic BMW) +0.783s
10. Ian Lowry (Padgetts Honda) +0.798s