The Portsmouth-based ship made the seizure as she returned to maritime security operations on the notorious drug smuggling route known as the 'Hash Highway'.
The Class-A drugs were estimated to have a street value of £9m.
The sale of heroin and other drugs of this kind is a known source of funding for terrorist organisations and criminal networks.
The drugs were destroyed following the operation.
"Heroin destroys lives but, thanks to the tireless work of HMS Dragon’s crew, these criminals will not be distributing this poison and will instead face justice," Defence Secretary Gavin Williamson said during a visit in the Gulf region.
"On closing, the flight observer was able to use the electro-optical device on the aircraft to provide high-quality images of the suspect dhow," said Pilot Lieutenant Scott Sunderland, from 815 Naval Air Squadron.
Sea bots were immediately launched on a mission and the Royal Navy and 42 Commando Royal Marines boarding team inspected the vessel.
Following the search of the dhow, which is a type of masted ship, the team found large quantities of drugs hidden in the vessel.
Boarding Officer Lieutenant Laurens Willaims said: "The team worked hard over long hours to ensure that any concealed narcotics were found."
"[The success of the operation] is a reward for the hours of training that have been invested by all in ensuring that these operations are conducted successfully," he added.