HMS Astute was on sea trials when her rudder is thought to have become stuck on a shingle bank between the mainland and the island off the west coast of Scotland. It is believed a crew transfer from the shore to the submarine was being carried out when the incident happened.
Royal Navy vessels and a tug helped free the submarine after an earlier attempt to tow the submarine failed, according to eyewitnesses.
A Navy spokesman described the accident as a "relatively minor incident", while a Ministry of Defence spokesman said: "This is not a nuclear incident. There are no injuries to personnel and the submarine is watertight."
The submarine weighs 7,800 tonnes, equivalent to nearly 1,000 double-decker buses, and is almost 100 metres (328ft) long. Its Spearfish torpedoes and Tomahawk cruise missiles are capable of delivering pinpoint strikes from 2,000km (1,240 miles).
The submarine's nuclear reactor means that it will not need refuelling once in its entire 25-year life and it makes its own air and water, enabling it to circumnavigate the globe without needing to surface.
John Ainslie, co-ordinator of Scottish CND, said: "This is just the latest in a long line of incidents involving nuclear submarines off the west coast of Scotland. These vessels are regular visitors to the seas around Skye.
"The Navy has several submarine trials areas near Raasay and Applecross. Inquiries into previous incidents have shown an appalling lack of common sense and basic navigation skills on these hi-tech submarines."
The grounding of the £1.2 billion Astute hunter-killer comes at the end of a dire week for the Royal Navy which has seen its carrier force halved, Harrier jump jets axed and warship force reduced by almost a quarter.
It is understood that the boat, which is first in its class, ran aground by its stern in a manoeuvre that “went slightly wrong” after it had dropped some sailors ashore in tidal waters off the Isle of Skye.
As the tide rapidly ebbed it is thought the skipper of Astute, Commander Andy Coles, decided not to power it off the obstruction as it would risk damaging the hull that carries some of the most advanced acoustic tiles that make Astute virtually undetectable beneath the seas.
Navy insiders insisted that there was no likelihood of a nuclear reactor leak or any other environmental issue.
No one was injured in the incident that happened earlier today. It came the morning after Trafalgar Day, where sailors celebrated the 205th anniversary of Nelson's victory.
“Astute ran aground by her very stern earlier this morning as she was transferring people ashore,” a Navy spokesman said. “There’s no nuclear issue or no environmental issue that we are aware of and no one has been hurt.”
The submarine, which carries a crew of 98, will now wait until later today for tug boats to pull her off when the tide comes in.
Astute, which was handed over to the Navy by its builders BAE Systems in late August, will then continue her sea trials.
It is not known whether the boat, which can carry up to 38 Tomahawk cruise missiles and Spearfish torpedoes, was carrying any weapons.
At 7,200 tonnes the Astute is the biggest British nuclear attack submarine ever built, although it is half the size of the Trident nuclear submarines at 16,000 tonnes. The boat’s nuclear reactor will never need refueling during its 35 year life.
Amid the gloom of Navy cuts, which will see the Senior Service reduced by 5,000 sailors to 30,000, there was some celebration following publication of the defence review on Tuesday after it was announced the seventh and final Astute-class submarine would be ordered.
However the incident comes on the back of a number of submarine accidents in the last few years.