Narine, 35, announced his retirement from international cricket in 2023, four years after playing his last match for West Indies against India
The match was set to start on 7:00pm local time at the Sher-e-Bangla National Stadium in Mirpur.
In the previous match at the ground, Australian women clinched their third successive T20 World Cup title by beating England by 6 wickets in the final.
Rain started soon after the match ended.
India have progressed to the final as the only undefeated team in the competition.
On the other hand, Sri Lanka won three of their four matches in the Super 10 group stage and overcame the defending champions, the West Indies, by 27 runs in Duckworth-Lewis method in a rain-marred semi-final clash last Thursday.