The bus was carrying twelve passengers, including ten from the mv Azura, when the accident occurred on the island of Dominica.
The names of the passengers involved in the incident have not been released.
Representatives from the cruise company are on-site at the hospital to support the injured. Next of kin have been informed, according to the line.
The company said in a Facebook posting:
“We'd like to advise you of some very sad news. A bus operated by a shore excursion provider was involved in a collision in Dominica on Wednesday lunchtime.
“The bus was carrying 12 passengers, including 10 guests from Azura. The cause of the accident is not yet known.
“One passenger has sadly died of their injuries. Another nine passengers were injured and treated at a local hospital, with the majority now discharged.
Azura is on a repositioning cruise to the Caribbean which left Southampton on October 28.