The 24-year-old Zakir was selected for the 17-person team after scoring 173 runs for Bangladesh A in the opening four-day match against India A in Cox's Bazar last week.
Tamim sustained the injury on Wednesday during a warm-up match at the same site. Taskin Ahmed, the fast bowler, was ruled out of the first ODI due to a back ailment earlier on Thursday.
After the ODI series between Sri Lanka and Afghanistan finished in a tie at Pallekele, Bangladesh was one of seven teams to earn straight qualification for the World Cup.
Dubai [UAE], May 25 (ANI): Sri Lankan all-rounder Angelo Mathews and Bangladesh batter Litton Das have made great advances in the ICC Men's Test Player rankings after delivering great performances in the first test match between their sides at Chattogram, which ended in a draw.
Dhaka [Bangladesh], May 18 (ANI): Mushfiqur Rahim on Wednesday became the first-ever Bangladeshi batter to score 5,000 runs in test cricket and also, the highest run-scorer for his side in the longest format of the game.