The left-arm pacer is expected to miss the opening matches of The Hundred, but the franchise will assess his fitness before deciding when he can return to action.
In a statement, Birmingham Phoenix confirmed that Mustafizur would join the squad as originally planned.
"Despite suffering an injury during Bangladesh's ODI against Zimbabwe on Monday, Mustafizur Rahman will join Birmingham Phoenix as planned. He has sustained a right hamstring tear and meniscal degeneration in his right knee, ruling him out of the remainder of Bangladesh's tour. He will travel to Birmingham next week for assessment by the Phoenix medical team."
Mustafizur featured in Bangladesh's first ODI against Zimbabwe but bowled only six overs before picking up the injury. He missed the second ODI, with the Bangladesh Cricket Board later confirming that scans revealed a Grade 1 tear in his right hamstring.
Team physio Bayjedul Islam said the pacer would return to Bangladesh to begin rehabilitation and is expected to be sidelined for around four weeks.
Although Mustafizur has received a No Objection Certificate (NOC) to play the entire 2026 season of The Hundred, the injury is likely to keep him out of the early stages of the competition.
Phoenix Performance Director James Thomas said the club remains hopeful the Bangladesh pacer will feature later in the tournament.
"Following discussions with Mustafizur and the Bangladesh Cricket Board, it has been agreed that he will travel to Birmingham next week for assessment by our medical team. After that, we will be able to determine whether he can take part in this year's The Hundred."
"We remain optimistic that Mustafizur will play for Birmingham Phoenix this season. At the same time, we will prepare for all possible outcomes while continuing to work closely with the BCB to assess his recovery and plan the best route back to cricket."