Sanjukta Digal was on her way to a polling booth when her vehicle was attacked by Maoists, media reports say.
Orissa is one of 13 states and union territories that are voting in this stage to elect a new parliament.
Powerful regional parties are on the ballot in 97 seats, and tens of millions are eligible to vote.
The election is taking place over seven stages, with votes being counted on 23 May. There are 900 million eligible voters, making this the biggest election the world has ever seen.
This election is widely being seen as a referendum on Prime Minister Narendra Modi, whose Hindu nationalist Bharatiya Janata Party (BJP) won a historic landslide in 2014.
Mr Modi will be hoping for a repeat performance.
But the kingmakers in this election are expected to be regional parties, which dominate politics in several Indian states and are fronted by charismatic local politicians.
Regional parties in states like Tamil Nadu in the south and West Bengal in the east are hoping to do well.