Organisers have taken the unusual step due to extreme weather conditions, meaning the series - currently locked at 1-1 - will become a four-game rubber.
"Due to extreme weather conditions, the BCCI has had to cancel the ODI. It is disappointing but we cannot overcome natural calamities," BCCI joint secretary Anurag Thakur told ESPNcricinfo.
"Even though the host association was hopeful of staging the match if weather cleared, the BCCI didn't want to take any risk."
West Indies lost the second encounter by 48 runs, with their frustration being added to when skipper Dwayne Bravo was fined 40 per cent of his match fee.
The Windies' over-rate was too slow and Bravo was penalised under a system that sees captains fined 10 per cent for every over their side is short.
The next encounter will take place in Delhi on October 11.