The latest COVID-19 cases in the squad, coupled with two players being ruled out due to injuries, resulted in the Ireland squad getting "severely depleted".
West Indies had won the opening ODI of the three-match series by 24 runs.
A joint statement issued by Cricket West Indies (CWI) and Cricket Ireland (CI) said on Tuesday (IST) that, "Two further positive COVID-19 cases were reported in the Ireland camp following recent testing, and two players being ruled out due to injury, resulting in Ireland having a severely depleted squad. The second CG Insurance One-Day International scheduled for Sabina Park on Tuesday, January 11 has therefore been postponed."
The two boards said that they were exploring possibilities to complete the series.
"CWI and CI are in discussions to review the match schedule and are working to explore all possibilities for the series to be completed. The five members of the Ireland team who have returned positive COVID-19 results remain in isolation under the care and supervision of the medical teams."
The Ireland squad had headed to Jamaica from Lauderhill, Florida at the end of last month after their ODI series against the United States had been cut short due to a COVID-19 outbreak.