One man was arrested following the shooting, said police, who were contacted by the Ministry of Defence about the incident.
There were no other details immediately released about the incident.
The Astute made headlines last year when it ran aground off the Isle of Skye, in northern Scotland, while doing sea trials.
Its nuclear propulsion system was not damaged in the incident and its reactor was declared safe, with no environmental impact. It was eventually pulled free and escorted back to port.