Bangladesh national team physio Delowar Hossain assessing the damage, ESPNCricinfo reported the news late on Sunday.
"Mustafizur suffered a clip fracture on his left thumb while playing his last match of the Indian Premier League yesterday," Hossain told the publication.
"This injury requires a period of rest and rehabilitation. As per our current assessment, he will be unavailable for selection for the next two to three weeks. We will conduct a follow-up evaluation after two weeks to monitor his recovery progress," he said.
Khaled Ahmed as replaced Mustafizur, who becomes the third player leave the squad for the series that begins on May 28 in Lahore.
Nahid Rana earlier withdrew for personal reasons, and Soumya Sarkar has since been ruled out with a back injury, and replaced by Mehidy Hasan Miraz.
Khaled comes off a strong domestic season, including a haul of 20 wickets in the recent Bangladesh Premier League.
Bangladesh play Pakistan in three T20Is in Lahore on May 28, 30 and June 1, and will be looking to bounce back after losing a T20I series 2-1 to UAE in Sharjah.
