Deputy superintendent of police Sushil Kumar said that the deceased were identified as Sumitra Devi, her sons Raja, Golu and daughter Sanju.
Kumar said that the house, which was in a dilapidated condition, caved in because of heavy rains in the past two days.
The two injured were admitted to a nearby hospital for treatment.
The bodies were sent for post mortem at Nalanda Medical College and Hospital, the DSP said.