In a tweet on Twitter, the MOD said: "It is with great sadness that the Ministry of Defence must confirm the death of an engineer from the RAF Aerobatics Team (The Red Arrows) in a tragic accident today".
'The pilot of the aircraft survived the incident and is now receiving medical care'.
It followed an incident at RAF Valley this afternoon.
Sky News Defence Correspondent Alistair Bunkall said it is believed the aircraft was a two person plane.
The Royal Air Force Aerobatic Team, known as the Red Arrows, fly over Scampton, Lincolnshire, Britain March 20, 2018 in this still image obtained from social media video.
A spokesman said they sent an emergency ambulance to the scene and Wales Air Ambulance is also in attendance.
Sian Rebecca Williams, 18, was waiting at Rhosneigr railway station when the jet flew overhead.
The air force says in a statement that "we are investigating the incident and it would be inappropriate to comment further at this stage".
"As I was looking I saw the parachute of one pilot open and then the plane hit the runway with a bang and a crumbling noise".
"I was watching the Red Arrow flying because you hardly ever see them and then it looked like it was about to land".
Their red single-engine jet trainers are a familiar sight at air shows and military events.
It is understood the aircrew had been at RAF Valley for routine Hawk simulator training - something that takes place once a month.
About 1,500 service personnel, civil servants and contractors work at the site.