David Paul and Michelle Calanog Paul from Fort Worth in Texas arrived in Fiji for a holiday on 22 May and reportedly died within days of each other.
The Ministry said it had advised the couple's family of their findings after an extensive investigation with help from the US Centre for Disease Control, the World Health Organisation and a medical forensics unit in Australia.
The Ministry said there was no risk to the public and the five people in contact with the deceased couple were under observation, but they are all in good health and have returned to work.
It said while infectious causes have now been ruled out, further investigations into the cause of the tourists' deaths are ongoing.
The family will be kept updated and the Ministry extends its condolences to them.