The soldier was from the 2nd Battalion the Duke of Lancaster's Regiment, which has been based at Weeton since 2011, a statement from the MoD revealed.
It continued: "The death occurred in Taji, Iraq, following an incident that is currently under investigation, but we can confirm that it was not as a result of enemy activity."
Officials have informed the soldier's family, who requested a period of grace be given before the name is released.
Around 150 soldiers from the battalion, known as '2 LANCS', began deploying to Iraq to fight against the so-called Islamic State - or Daesh - last month.
After training for several months in the UK, the soldiers set off for a six-month tour to train Iraqi and Kurdish security forces as part of a larger 500-strong British Army force.
They are also expected to provide protection to other British troops in the country.
Speaking last month, defence secretary Sir Michael Fallon said: "Defeating Daesh will help stabilise Iraq, which in turn will make Britain safer, and 2 LANCS should be proud of the role they'll play in helping achieve that goal.”
Major Rob Singleton, Commanding Officer of 2 LANCS, added at the time: “Our role in Iraq is vital.
"We are part of an international coalition and will contribute by training the Iraqi and Kurdish security forces in diverse skills. This includes counter IED (improvised explosive devices), infantry, and medical training.
"We are well prepared. As we demonstrated with the floods in the north of England last Christmas, we relish a challenge and the Kingsmen - our soldiers - can make a real difference. We feel proud to have been chosen for this task and are keen to get started.”