The woman was trapped underneath the car that was allegedly driven by her "life-long friend".
She was pronounced dead on the scene after fire services removed her from underneath the vehicle.
Devon and Cornwall Police said they were called to the car park at All Saints' Church on Exeter Road in Exmouth on Tuesday at 4:45pm.
According to the church, the victim and the driver, who is also 84-years-old, were life-long friends and were attending an over 60s event in the church hall.
In a statement, Fr Owen Murphy of All Saints' Church said the community was "devastated" by what happened.
"The church community at All Saints Church, Exmouth, is saddened and devastated by the tragic collision on 10 December, involving two life-long friends, following a local over 60s group Christmas event which had been held in the church hall.
"Our thoughts and prayers are with the family and friends of those involved. I would like to commend the members of the emergency services who dealt with the collision and the church members at the scene who were quick to offer care and support in what was a distressing situation for everyone there."
No arrests have been made. Police are investigating.
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