Aldi opened its store near Milton Drive last year after securing planning permission in 2019.
As part of the same application, outline permission was secured for a care home to the south of the site.
But Markden City Homes has instead now submitted a planning application to build 26 homes on the vacant site, prompting concerns from residents living nearby.
Market Drayton's Mayor, Councillor Roy Aldcroft had welcomed the proposals for a care home at the time, saying it would be a "welcome addition to very stretched facilities in the area".
He said he has been contacted by several residents who are unhappy with the latest plans for houses.
A number of objections have been lodged on Shropshire Council's website, with reasons including the potential to cause traffic and parking problems.
Fears have also been raised about 'overcrowding', with one objector saying consideration should be given to reducing the size of the development.
Councillor Aldcroft said: "The residents are up in arms. They are concerned that it will increase pedestrian footfall considerably, so there will be a lot more people walking past their houses.
"In addition to that, traffic will increase and it is felt to be out of touch with the design or ethos of the area.
"They are disappointed and surprised this has come forward. They were expecting a nursing home to follow the completion of the Aldi. We do need a nursing home within the town somewhere."
The plans state there would be a mix of three and four-bedroom homes, 21 of which would be for affordable rent and five for rent-to-buy.
They would be managed by the Wrekin Housing Group.
A design and access statement, submitted with the planning application, says: "The proposed dwellings would be sited in a cul-de-sac formation with off road parking provided for each of the dwellings proposed and private amenity space located to the rear of each of the proposed dwellings.
"The proposed dwellings would be simple in form and appearance in keeping with the existing dwellings located on Milton Drive. The proposed materials pallet and proposed dormers in the roof space are in keeping with the existing development located to the west and are considered to be appropriate in terms of character and appearance.
"The proposals would deliver 26, much needed affordable homes in a sustainable location."
Shropshire Council is due to make a decision on the planning application in the upcoming months.