The left-arm seamer complained of pain while bowling during the first ODI against Zimbabwe on Monday, and subsequent scans revealed that Mustafizur will be sidelined for the next four weeks.
Bangladesh lost the one-off Test in Zimbabwe and are already 2-0 down in the three-match ODI series, with the final game set to take place in Harare on Saturday.
The teams will then move on to Bulawayo for a three-match T20I series that starts Wednesday.
After Bangladesh's tour of Zimbabwe ends on July 19, they are set to tour Australia for two Tests from August 13, with both matches part of the World Test Championship cycle.
Zimbabwe fast bowlers Richard Ngarava and Newman Nyamhuri scored vital lower-order runs and then shared five wickets as the home side edged Bangladesh by 25 runs in the first of three ODIs in Harare.
Innocent Kaia struck a maiden century before the bowlers starred as Zimbabwe recorded their biggest ever Test victory after thrashing Bangladesh by an innings and 85 runs in Harare.
The South African Women were made to work hard for runs as they eventually chased down 117 to defeat Bangladesh by four wickets in the Women's T20 World Cup at Lord's on Sunday.
Matt Renshaw struck a career-best 89 not out from 52 balls to help Australia beat Bangladesh by seven runs in the second T20I as the visitors took an unassailable 2-0 lead in the three-match series.
