All-rounder Naeem Islam and left-arm spinner Mohammad Sohrawordi were also excluded, while middle-order batsmen Roqibul Hassan, Faisal Hossain return alongside paceman Nazmul Hossain.
Ashraful paid the price for his poor performance in the test series against England where he made 50 runs from four innings, and followed up at the Asia Cup with 29 runs from two matches before being dropped for the third.
Roqibul returns to the side three months after he retired from all cricket in March, then changed his mind a week later, only to be banned by the Bangladesh Cricket Board until June 30 for upsetting the team's plan.
Left-handed Faisal Hossain returns after almost six years, having played the last of his four one-day internationals against Pakistan in 2004.
Bangladesh start their campaign with a warm-up match against Sussex on July 3 before playing three ODIs against England and further ODIs against Ireland in Belfast.
They will end the tour with two ODIs against Scotland and the Netherlands respectively on July 19 and 20 at Glasgow.
Squad: Tamim Iqbal, Imrul Kayes, Zunaed Siddique, Roqibul Hassan, Shakib Al Hasan, Mushfiqur Rahim, Mahmudullah, Faisal Hossain, Jahirul Islam, Masrafee Mortaza, Rubel Hossain, Shafiul Islam, Nazmul Hossain, Abdur Razzak, Syed Rasel.
England coach Capello's father was Nazi prisoner
England vs. Germany clash pulls record punters
Morgan helps England go 2-0 up on Australia
Beer behind England's new found success at WC
Messi mesmerises but bungle costs England