Police were called to the shop in Lindängen in the south of the city just before 1am on Monday.
Bomb technicians analysed what police described as a jar-like object, believed to contain explosives.
But Kim Hild, a press officer for the TT news agency said on Monday morning that following their investigation, “nothing suggests it was explosive”.
The suspect bomb was discovered following a new wave of unrest in the city’s suburbs, in a month already punctuated by several large fights, shootings and explosions.
Overnight three cars were set on fire, with at least one other vehicle damaged by the flames.
Police said on Monday that it was unclear if the fires were linked to the suspected bomb at the grocery store.
Last week a youth community centre and several cars were set alight in the suburb of Kroksbäck in Malmö, days after hand grenades were thrown in the same area, which is around six kilometres away from the scene of the most recent unrest.
The southern Swedish city has experienced growing violence in recent years. Some of its inner-city areas and suburbs have a reputation for gun and gang-related crimes as well as race-related violence between different immigrant groups.
As a result, the force has recently stepped up its presence in known trouble-hit areas.