The crew were from HMS Vigilant, one of four Royal Navy submarines which operate the Trident nuclear missile system.
"We do not tolerate drugs misuse by service personnel. Those found to have fallen short of our high standards face being discharged from service," a Royal Navy spokesman said.
The Daily Mail newspaper reported that the sailors had failed drugs tests while the submarine was docked in the United States to pick up nuclear warheads and undergo work, and the sailors had been accommodated in hotels on shore.
A defence ministry spokesman declined to comment on the location of the incident but said: "There is no evidence to suggest any individual was under the influence while performing their duties."
Britain's four nuclear-armed submarines each carry eight operational missiles and 40 nuclear warheads, and have a crew of 135. Since 1969 Britain has had at least one nuclear-armed submarine on patrol at all times.