A woman in her 30s died in the Royal Artillery Barracks in Larkhill garrison, the Ministry of Defence (MoD) said.
Emergency services were called to the barracks on Salisbury Plain at 12.20pm on Thursday.
Wiltshire Police said it was not treating the death as suspicious.
A police spokesperson said: “We were called to Larkhill Garrison yesterday following the sudden death of a woman in her thirties.”
They added: “Our thoughts are with her family and friends at this difficult time. We would ask that their privacy is respected.”
In a statement, the MoD confirmed that the soldier died on 22 July.
It added: “The circumstances surrounding this death are being investigated and it would be inappropriate to comment any further at this time.
“Our thoughts are with the soldier’s family and friends at this difficult time.”