The RAF said a full independent inquiry was being launched into the incident at RAF Scampton in Lincolnshire.
The tragic accident came less than three months after another pilot with the world-famous aerobatics team, Flight Lieutenant Jon Egging, 33, was killed in an air show crash in Dorset.
Medical teams rushed to RAF Scampton, the base of the Red Arrows, after the incident at about 11am yesterday.
The Lincolnshire and Nottinghamshire Air Ambulance airlifted the pilot to Lincoln County Hospital but his injuries were so severe that he could not be saved.
The Red Arrows completed their final display of the season in September and are carrying out their winter training.
Group Captain Simon Blake said: “The pilot was ejected from the aircraft whilst the aircraft was on the ground.
“The director-general of the Military Aviation Authority is in the process of initiating a full and independent service inquiry to determine the cause of this tragic incident. It would be inappropriate to speculate on the cause of the incident until that inquiry is complete. The investigation will determine the facts.
“The pilot’s next of kin have been informed. Our thoughts and prayers are with the pilot’s family and friends at this difficult time.”
The pilot is expected to be named later today.
The Red Arrows Hawk T1 jets could be seen lined up on the tarmac at a misty RAF Scampton after the accident. One of the aircraft had the front part of its canopy missing.
Flt Lt Egging crashed to his death on August 20 minutes after performing a display with the Red Arrows watched by his wife.
Eyewitnesses described seeing the aircraft flying low before smashing into a field and coming to a standstill with its nose in the River Stour near the village of Throop.
Hundreds of RAF servicemen and women joined family and friends at a memorial service in Lincoln Cathedral last week.