The unnamed civilian pilot landed at RAF Valley, on the island of Anglesey, on May 25 having made the 290-mile trip from an airfield in Surrey.
It sparked an emergency response from Ministry of Defence guards and fire crews, the Royal Air Force confirmed.
The base was closed for maintenance and crews believed the single-engine turboprop plane had made an emergency landing.
But it is understood that he actually taxied the jet to the far side of the airfield, near the beach.
He told guards when confronted that he made the trip “to go to the beach”, according to a Defence Aviation Safety Occurence Report, despite this breaching the more stringent lockdown rules in Wales.
After security checks were carried out, the pilot decided to take off again, despite the airfield remaining closed, the RAF said.
North Wales Police said they are “considering” whether there were “potential breaches” of the Welsh Covid-19 legislation, which bans people from driving more than five miles and has closed beauty spots.
An RAF spokesman said: “The RAF can confirm that, on May 25, a civilian PC-12 aircraft landed on a closed runway at RAF Valley without permission.
“Whilst irregular, it was assessed that there was no threat to station personnel or the wider public. The incident has been reported to the Civil Aviation Authority (CAA).”
While the RAF does accept civil aircraft at its stations, 24 hours’ notice is required to ensure they do not affect military activity, and the RAF said appropriate fire and rescue cover was not in place as a result.
Superintendent Richie Green, from North Wales Police, said: “We were contacted by colleagues from RAF Valley at 1.04pm on Monday 25 May, reporting that a light aircraft had made an unauthorised landing at the airbase. The pilot was dealt with by military police.
“Whilst the incident is primarily being investigated by the RAF and Civil Aviation Authority, North Wales Police are currently considering potential breaches of the Covid legislation in Wales.”
RAF Valley is home to the No 4 Flying Training School, which trains fighter jet pilots and crew for maritime operations, and Prince William was posted there in 2010 with Number 22 Squadron to fly the Sea King 3A helicopter.