Tamim, 34, who retired in a shock move in July before reversing his decision a day later at the request of Bangladesh Prime Minister Sheikh Hasina, returned to the side only last week for the opening two matches of the just-concluded home series against New Zealand.
Tamim established himself as one of the country's most dependable players and is the only Bangladeshi to score centuries in all three formats of the game.
But he took a break from Tuesday's final match that Bangladesh lost by seven wickets in Dhaka, and reportedly refused to give a guarantee of his participation in all matches in the World Cup.
Top-selling Bengali newspaper Prothom Al reported on Tuesday that coach Chandika Hathurusinghe and skipper Shakib Al Hasan said only fully fit players could be in the World Cup squad, leading to the exclusion of Tamim.
"Tamim Iqbal has had an injury concern for a long time, which we know," chief selector Mihajul Abedin said.
"He was fighting against it and got back to fitness ahead of the New Zealand series. But after the first game, he complained of injury again."
New Zealand whitewashed Bangladesh to win the three-match series 2-0.
Batsman Najmul Hossain Shanto, who made his debut as captain during the series against the Kiwis, has been named as vice-captain for the World Cup.
The Bangladesh side travels to Guwahati on Wednesday for two warm-up matches against Sri Lanka on September 29 and against England on October 2, before the World Cup begins on October 5.
The side will then move to Dharamshala for their tournament opener against Afghanistan on October 7.
Squad
Shakib Al Hasan (c), Liton Das, Tanzid Hasan Tamim, Najmul Hossain Shanto (vice-captain), Towhid Hridoy, Mushfiqur Rahim, Mahmudullah Riyad, Mehidy Hasan Miraz, Nasum Ahmed, Mahedi Hasan, Taskin Ahmed, Mustafizur Rahman, Hasan Mahmud, Shoriful Islam, Tanzim Hasan Sakib.
