Reports suggest the pilot ejected from the aircraft before the plane crashed. However, there are claims two people were onboard the Hawk jet.
Witnesses reported the jet smashed onto the runway before it went "up in flames".
A spokesman for the Welsh Ambulance Service said: "We were called shortly before 1.30pm this afternoon to reports an aircraft had crashed at RAF Valley in Holyhead.
"There is an emergency ambulance and a Wales Air Ambulance at the scene."
The condition of those in the accident is not yet known.
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The accident happened near Llangollen.
Aviation website Airlive said the plane was Hawk Red3.
The Ministry of Defence has confirmed the incident.
A MoD spokesman said: “We are aware of an incident today at RAF Valley involving a Hawk aircraft.
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“We are investigating the incident and it would be inappropriate to comment further at this stage."
Eyewitnesses said they saw the plane explode.
An eyewitness told the Daily Post: “I was sat at Rhosneigr train station waiting for the train and you can see the airfield from there.
“I was watching the Red arrow flying because you hardly ever see them and then it looked like it was about to land then next thing I saw was the parachute and then the plane hit the runway and went up in flames.”
Pictures from the scene show a huge plume of smoke billowing into the air fro the runway.
The jet was flying from RAF Valley back to RAF Scampton in Lincolnshire when the accident took place, according to the BBC.
The iconic Red Arrows is the RAF's aerobatic display team which performs stunts and daredevil displays at events like the Trooping the Colour Ceremony in London in distinctive Hawk fast-jets.
Based at RAF Scampton in Lincolnshire, all Red Arrows pilots have flown operationally in frontline aircraft before joining the display team.
More to follow...