After continuing to struggle with the injury over the past few weeks, Yeates was left out of City's travelling party to Scunthorpe United this Tuesday.
Along with missing the Scunthorpe match, Yeates was also allowed a couple of days away from the training ground to further investigate what is best long-term for his troublesome shoulder.
Following his absence from the Scunthorpe match, Yeates returned to training at the back end of this week but it is still unsure as to whether he will be deemed fit enough to feature at the Coral Windows Stadium this Saturday.
Parkinson said: "We gave Mark Yeates a few days off during the week to allow him to make the right decision over his shoulder.
"We have been advised that he needs to get his shoulder operated on and he is going to see a specialist about it next week.
"Hopefully he will get it fixed soon but he has trained with us Thursday and Friday.
"He is fine to train with it but we just wanted him to be clear in his head and make sure he is doing the right thing for himself going forward."
Filipe Morais is expected to be sidelined still with a knee injury, while Rory McArdle is definitely ruled out as he completes a two-match ban following his recent red card at Sheffield United.