The legislator had hosted the feast at her home in Chukti village of the district.
Eyewitnesses said that a large number of people gatecrashed her house when blankets were being distributed among citizens by the MLA after the feast.
In the melee, the elderly woman and three others fell on the ground and people ran over them.
Superintendent of Police Mithu Prasad said that the cause of the stampede was being probed.
The dead woman has been recognised as Dani Devi (65) of Sansarpur village, he said adding her body has been sent for post mortem.
The injured were treated at Sadar hospital of the district.