The restaurant and takeaway will be the area's first formal seated eatery and will create several new jobs.
But St Paul ward councillor Lucille Thompson said that drive-in collections could cause traffic problems on nearby junctions, while smells and noise from an outdoor seating area would disturb residents at night.
Applicant Andrew Smith said: “This is not a restaurant aimed at a rowdy clientele. We're not looking to the after-pub market at all.”
The pizzeria will serve upmarket Italian dishes.