Officers were called to the scene at HM Naval Base Clyde, known as Faslane, at around 12.30pm on Thursday.
A post-mortem examination will be carried out and the death is currently being treated as unexplained.
Faslane is home to the UK’s nuclear submarines and the core of the submarine service.
A Police Scotland spokeswoman said: “A post-mortem examination will be carried out to establish the exact cause of death which is currently being treated as unexplained.
“A report will be submitted to the procurator fiscal.”
A Royal Navy spokeswoman said: “We are aware of an incident and cannot comment further at this stage.”