The 23-year-old left arm bowler sprained his ankle warming up for a Dhaka Premier League match on Thursday, joining a growing injury list which includes batsman Mahmudullah Riyad and pace bowler Rubel Hossain.
Bangladesh had previously barred the injury-prone Mustafizur from playing in the Indian Premier League ahead of the World Cup, which starts May 30. It had let him take part in the domestic 50-over league to keep match-fit however.
The new injury is expected to sideline him for at least two weeks.
Rubel Hossain has been suffering from a side strain.
"We hope to start his training session within a day or two," said Debashis.
Off-spinner Mehidy Hasan hurt his thumb in a league game last week but returned to action on Monday.
However, Debashis was hopeful all of the squad would be match-fit for the tournament.
"With the amount of time we have and the current improvement rate of the players, I don't think any one will miss the World Cup," he said.
"We hope we can field all our regular players in the tri-nation and World Cup. We hope to announce the squad in a day or two," said chief selector Minhajul Abedin.
The deadline for announcing World Cup squads is April 23, but teams can be changed up to May 23.
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