Mustafizur complained of pain after joining the national training camp last week, at the end of the Indian Premier League (IPL) in which he played for Mumbai Indians.
"Subsequent tests have revealed a crack on his left big toe which will sideline him for a few weeks,” said a Bangladesh Cricket Board (BCB) statement.
"It takes around three to four weeks to recover from such injuries and therefore he can't play against Afghanistan," BCB senior physician Debashis Chowdhury said in the statement.
Mustafizur is expected to start rehabilitation in two weeks, the doctor added.
Afghanistan will host Bangladesh for the first T20 series between the two countries in the Indian city of Dehradun from June 3 to 7.
Afghanistan will be preparing for their first-ever Test, against India in Bangalore from June 14.
Afghanistan are ranked eighth in Twenty20 internationals, two places ahead of Bangladesh who left for India on Tuesday.
First Published: May 29, 2018, 2:42 PM IST