South Kirkby Health Centre, which is now closed, could be knocked down to make way for a Co-op food store at the site, on Barnsley Road.
A decision on the plan is due to be made on Thursday, but 134 local people have signed a petition opposing it.
They say that the supermarket would increase traffic to intolerable levels and increase noise for people living nearby.
South Kirkby councillor Michelle Collins said she was “deeply concerned” by the Co-op’s plans.
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She said: “Residents are already contacting me about the rush hour traffic in the area, and that’s only going to get worse.
“We already have lots of shops and local convenience stores and I don’t think we need another one.
“We want to be supporting little local businesses and I think this could really have a detrimental impact on them. That in itself is a worry.
“I understand that the building needs to be brought back into use and it shouldn’t be derelict. But we have enough shops already.”
Despite the concerns, the application has been recommended for approval by councillors, albeit with 28 strict conditions attached.
Among these is a rule preventing deliveries at certain times of the day, and limiting the store’s opening hours to between 7am and 10pm.
In a report for the planning committee, it’s said that the council highways staff accept that there will be an increase in traffic on the road, but that the number of extra vehicles passing through the area will be “relatively few”.
The Co-op have been contacted for comment.