With City two goals up at Doncaster's Keepmoat Stadium at the time, Yeates was replaced with Tony McMahon as a precaution by Parkinson after the Irishman fell awkwardly on his shoulder.
City host second-placed Preston North End at the Coral Windows Stadium this Easter Monday (kick off 3:00pm).
Yeates scored the winner the last time City and Preston met when Parkinson's men impressively defeated the Lilywhites 2-1 at Deepdale back in November.
Parkinson said: "Yeatesy just fell on his shoulder in the second half and with us winning the game at the time, we didn't want to take any chances so we brought Tony on."
City will have to assess the fitness of Gary MacKenzie ahead of Monday's visit of Preston after the giant Scot took a whack to his ankle while scoring the opening goal at Doncaster.
Jak Alnwick will be unavailable to the Bantams for the rest of the season after the loanee goalkeeper returned to Newcastle United on Friday to have surgery on a wrist injury which will sideline him for the remainder of the campaign.