“The 31-year-old right-handed top-order batsman will remain in Trinidad to continue his rehabilitation,” the WICB said.
“A replacement player will be named in the coming days,” it said in a statement.
Simmons, who has played 34 T20Is with a top score of 77, joins all-rounder Kieron Pollard on the sidelines after a knee injury forced him to decline signing a player contract for the tournament in India.
Spinner Sunil Narine, who is still working to fix his illegal bowling action, and Darren Bravo, who has opted to focus on the longer formats of cricket, withdrew from the West Indies squad last month.
The Caribbean team, currently in Dubai, are due to arrive in Kolkata on March 7 ahead of the global event which they won in 2012.
West Indies will have warm-up matches against India next Thursday and Australia on March 13.
They have been drawn in Group One of the Super 10 stage where they will play alongside England, South Africa, Sri Lanka, and one of the qualifiers from the first round.
Darren Sammy (captain), Samuel Badree, Sulieman Benn, Carlos Brathwaite, Dwayne Bravo, Johnson Charles, Andre Fletcher, Chris Gayle, Jason Holder, Ashley Nurse, Denesh Ramdin, Andre Russell, Marlon Samuels, Jerome Taylor.