Local media reported the bus was traveling on a road connecting the town of Budva, on the Adriatic Sea coast, with Cetinje which is located in a mountainous inland area.
“I was listening to music and all was normal. Then all of sudden there were screams and the sound of glass breaking,” one of the passengers told the state RTCG radio.
It was not immediately clear what caused the bus to skid down some 15 metres into the ravine.
Photos showed rescue workers holding on to a metal wire to try to reach the wreckage.Doctors said nine people have been seriously injured, including one in life-threatening condition.
Prosecutor Andjela Radovanovic told reporters the two people killed were a British national and an unidentified woman.
Police said on X, formerly known as Twitter, the two victims died on the spot while the injured received aid in Cetinje.
The seriously injured were later transferred to a hospital in the Montenegrin capital Podgorica.