Rashid pulled out of the matches scheduled at Emerald Headingley for Friday night and Sunday afternoon and has been referred back to England’s medical team as a centrally-contracted player.
The 31-year-old was affected by the problem during the World Cup and announced himself unfit to play for Yorkshire after a practice session.
Rashid is out of contract at the club at the end of the season and it remains unclear whether he wants to play County Championship cricket going forward, having lost his Test place earlier this year having previously indicated that he wants to pursue a white-ball only path.
“Adil practised on Thursday and said that his shoulder is worse than it’s been for some time and declared himself unfit,” said Martyn Moxon, Yorkshire’s director of cricket.
“We’ve referred him back to England and are now awaiting the outcome of the scan.”
Rashid was granted a fortnight’s break after the World Cup after needing pain-killing injections during the tournament.
The injury affected his ability to bowl his variations and he was not at his best during the competition. Yorkshire plan to wait until England announce their next batch of central contracts this autumn before discussing with the player his future at Headingley.
“We’ll basically assess things once the England contract situation is resolved,” added Moxon.
Yorkshire have re-signed the South African spinner Keshav Maharaj for their next two Championship games at home to Nottinghamshire at Scarborough from August 18 and away to Somerset at Taunton from September 10.
They are also considering the possibility of signing another overseas player for their final two Championship matches at home to Kent and away to Warwickshire.