Broad, suffering from patellar tendonitis in his right knee, missed the last two games during the tour of West Indies and will also miss Tuesday's warm-up match in the tournament against the same opponents in Fatullah.
But the 27-year-old fast bowler said he will "definitely" be fit for the warm-up match against India in Mirpur on Wednesday.
"I've had an injection in my knee last week, generally they're eight to 10 days, but with the flight we obviously left Barbados I think Friday afternoon and what are we now, Monday morning?" Broad told reporters in Dhaka.
"It was quite a long travel so obviously I had to manage that well.
"It's unlikely that I'll play tomorrow because I haven't actually run on my knee since I've had the injection yet, but I'd say I'll definitely play against India the next day."
England, who lost the three match T20 series in West Indies 2-1, will begin their campaign in the World Cup on Saturday against New Zealand in Chittagong.
"The soreness has gone a little bit, we had 12 hours in Dubai in which I managed to get a gym session...so it seems to be progressing pretty well," Broad added.
"If it was a Test match tour it might be more concerning but with it only being four overs a game I'm pretty confident I'll be able to play a full part in this World Cup."
Image: Stuart Broad
Photograph: Gareth Copley/Getty Images
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