The warship left Devonport on Tuesday and will head to Australia, the Far East and the Persian Gulf region over the next seven months.
It is one of two vessels being deployed to the Pacific amid escalating tensions with North Korea.
In August, Theresa May promised Japanese prime minister Shinzo Abe she would send HMS Argyll to the region to join British allies already stationed there following a series of provocative missile launches.
Last month, Britain’s new defence sectary Gavin Williamson spoke of his pride that the two British vessels – both equipped with SeaCeptor missile defence systems – will be deployed in the region in the battle to rein in North Korea’s threatening behaviour.
Mr Williamson said: ”We have got HMS Argyll, HMS Sutherland going up to the region to do operations with our allies.
“That is something I am very proud that we are doing and we are going to continue to do.”
The Royal Navy says HMS Sutherland will conduct operations and exercises with a wide range of allies and partners during the tour.
Commander Andrew Canale, the ship’s captain, said: “This is an opportunity for HMS Sutherland to demonstrate the global reach of the Royal Navy as well as the UK’s commitment to building relationships and maintaining stability in the Asia-Pacific region.
“A deployment of this nature means that we must be prepared to respond to any eventuality. I am very proud of the Ship’s Company and the many support organisations who have assisted HMS Sutherland to deploy two months ahead of her planned departure date.
“Having just returned from Christmas leave, I am acutely aware of the sacrifices that our families are also making and I am grateful for their support as we embark on this period away from home.”
Engineering Technician Josh Reed has been serving on board HMS Sutherland for three years.
He told the Plymouth Herald: “I was originally going to leave the ship on the day before deployment but I requested to stay on board for longer. I’m really pleased that I am now staying to the end of the trip and I’m looking forward to visiting places that I haven’t been to before.”
HMS Sutherland, a Type 23 frigate, is part of the core of the Royal Navy’s destroyer and frigate fleet and the ships versatility makes it a useful asset in war-fighting, peace-keeping and maritime security operations around the globe.