The concierge of the building in Tiefenau called the police around 11.30am after finding the explosives during a clear-out of the attic room, which was due to be renovated, reported news agency ATS.
The building’s residents were evacuated while the army examined and identified the munitions, confirming they were German grenades made in 1938.
One was in a decent state, while the other was less likely to function, army spokesman Daniel Reist told ATS, adding that it was not known how they came to be in the apartment block.
The explosives were transported to the army base at Thun where a specialist unit would carry out a controlled explosion.
It’s rare that Second World War explosives are found in Swiss urban areas, said the spokesman, though the army does sometimes deal with munitions found in the countryside.