Lidl aims to demolish part of the former Fitness First gym in Cathcart Road, Govanhill, at the edge of the main shopping area, creating 20 full-time jobs.
It will build a small extension, but otherwise there will be little change to the building.
But small local traders believe the supermarket will hit their business and point out there are already other supermarkets within walking distance.
Residents also fear there will be an increase in traffic on what is a congested stretch of road.
Senior planner Ken Clark told councillors the supermarket would attract people to the area and could benefit existing shopkeepers.
He said: "This is a retail type that is not in the area now. It has the potential to increase the attractiveness of Govanhill by maintaining expenditure in the area, decreasing trips to other areas and increasing footfall.
"A traffic assessment was submitted and it showed the projected increase in traffic could be accommodated and none of the junctions would be over capacity as a result of this development."
But Southside Central councillor Jahangir Hanif insisted the supermarket would impact on local traders.
He said: "Unfortunately, the recession and local problems already make it difficult for small businesses to survive."
Mr Hanif said 28 shops in the area had closed and planning permission had recently been granted for two large supermarkets in Govanhill.
Fellow Southside Central councillor Mhairi Hunter said: "It is by supporting the small traders that we can help with the regeneration of the area."
Mr Clark said a retail survey carried out last year showed vacancy rates in Govanhill are at 10.7%, against the national average of 14%
He added: "In terms of vacancies, Govanhill is not performing too badly."
Councillors agreed by a majority vote to grant planning permission for the supermarket.