West Yorkshire Police confirmed they attended Morley’s rugby and cricket ground in Scatcherd Lane at 2.23pm on Sunday in response to the incident.
It is understood that the man, who is thought to be in his 50s, lost three fingers and part of his palm.
He was acting in the display as part of the Northern World War 2 Association.
Blogger Graham Tyler, who was at the event, wrote: “One of the soldiers was severely injured by an explosion from a Mortar being used in the display.
“Hundreds watched while the casualty was treated by first aid personnel on site until the arrival of the West Yorkshire ambulance responders, backed up by ambulance crews.
“People were shocked and one eye witness described the scene as horrific. The event field was cordoned off eventually and all anxious on lookers removed from the area.”
It is thought the man’s son was also affected in the incident
The event was halted and onlookers asked to move away from the scene.