The middle-order batsman, who failed to impress in Test and one-day series in Sri Lanka last September, was replaced with all-rounder Alok Kapali in a 15-member squad led by Habibul Bashar.
Imran has so far scored 523 runs in 33 one-dayers with an average of 16.34.
Kapali, a middle-order batsman and a leg-spinner, returned to the squad after playing in a home one-day series against Zimbabwe in January 2005.
Bangladesh, who lost both the Test and one-day series in Sri Lanka, will play three one-dayers against the visitors on February 19, 20 and 24. The sides will then clash in a two-Test series.
The hosts have won just 10 of their 115 one-dayers, including a memorable victory over world champions Australia in a tri-series match in England last year.
Bangladesh have lost 35 and drawn four of their 40 matches since gaining Test status in 2000. Their lone win came against a depleted Zimbabwean side at home in January 2005.
Squad: Habibul Bashar (capt), Khaled Mashud, Khaled Mahmood, Mohammad Ashraful, Javed Omer, Rajin Saleh, Aftab Ahmed, Shahriar Nafees Ahmed, Mohammed Rafique, Manzarul Islam Rana, Mashrafee Mortaza, Nazmul Hossain, Alok Kapali, Abdur Razzak, Syed Russel.
Coach: Dav Whatmore.