"I am resigning from my post today with a heavy heart," he told reporters in Lahore.
Kohli's compatriot and veteran pacer Ashish Nehra have been named as the 11th man in the squad, ICC said in a release on Monday.
Carlos Brathwaite hit four consecutive sixes as West Indies scored 24 off the final over to beat England in an astonishing World Twenty20 final.
Having slayed the giants of ICC T20 World Cup 2016 -- India and New Zealand -- in their respective semi-finals, West Indies and England clash in the final of the tournament at the iconic Eden Gardens on Sunday.
Lendl Simmons scores unbeaten 82, off 51-ball as West Indies beat India by seven wickets, and make second World T20 final.
Jason Roy muscles England to 7-wicket win over New Zealand in semi-final 1 of T20 World Cup 2016 to qualify for final
The second World T20 semi-final is likely to hinge on who emerges on top in the battle between the big-hitting West Indian batsmen and India's wily spinners in Mumbai on Thursday.
Kohli had entered the ICC World T20 tournament 24 points behind Aaron Finch, but has now opened up a 68-point advantage over the Australian.
England hope in-form batsman Joe Root and "home" advantage can make the difference against undefeated New Zealand in the first World Twenty20 semi-final on Wednesday.
South Africa thrashed Sri Lanka by eight wickets in their final game at the World Twenty20 in Delhi on Monday.