After suffering with the issue earlier this season, Yeates' shoulder twice popped out of place during the Easter double-header against Doncaster Rovers and Preston North End.
Since then, City have tried their best to look after the injury, with Parkinson conceding that Yeates will probably have to undergo an operation eventually.
Parkinson said: "Yeatesy is unlikely to start on Tuesday.
"We'll probably just use him from the bench if we can. He is training fine with it but we have to be careful.
"He is due to see a specialist this week about his shoulder and I believe he will end up having to have surgery on it."
James Meredith and Christopher Routis are slight doubts for Tuesday's match at Scunthorpe due to knocks picked up against Sheffield United at the weekend.
Filipe Morais is definitely ruled out of the trip to Glanford Park as City aim to finally rid the Portuguese winger of a long-standing knee injury.
Parkinson added: "Fi's knee isn't still completely right.
"He hasn't been totally comfortable with it since injuring it at (Leyton) Orient back in February.
"He had a pain-killing injection to get him through the Bristol City match but it has flared up again for him.
"We don't feel it is anything long-term but we do need to investigate it further now and get to the bottom of the issue."