Danish media reports said earlier that the tourist, Joachim Loevschall, 26, was apparently shot by soldiers after entering the zone and ignoring warnings to leave.
Cuban Foreign Ministry spokeswoman Marianela Ferriol was quoted by the Cuban news agency Prensa Latina as saying the incident occured at dawn on March 29.
Ferriol did not give further details of the incident, or say where it took place, noting the dead man's family had asked for the Cuban Foreign Ministry to handle the case with extreme discretion.
Ferriol said the Dane was not carrying any documentation at the time of the incident and so was not identified until last Friday. Ferriol added the ministry had immediately informed Danish authorities of the incident and begun an investigation into the case.