The incident took place in Sambasivapet under Kothapet Police station limits when the two-storeyed structure came down crashing around 5 AM when the victims were fast asleep, police said.
The deceased have been identified as Thumati Anjamma (70) and her grandson Geethapratap (3).
The building, which was under dispute since the landlord's demise recently, was occupied by Thumati.
According to locals, heavy rains have been lashing Guntur since a week following which the old building gave away.