The office said 12 Britons, two Ecuadorian nationals and a French citizen were injured. A Foreign Office spokeswoman said the Britons' injuries were non-life threatening.
Staff from the British Embassy in Quito were working with a tour company to inform the passengers' relatives.
The office could not say whether the passengers were tourists and that it would not release the name of the tour company until all the next of kin were notified.