Afghanistan will host Bangladesh for the first-ever T20 series between the countries in the Indian city of Dehradun from June 3 to 7.
A week later Afghanistan will play their inaugural Test, against India in Bangalore from June 14.
Selectors delayed announcing Mustafizur's replacement until learning more about the newly-laid pitch at Dehradun's Rajeev Gandhi International Stadium.
"It was a new ground so we wanted feedback from the team," said chief selector Minhajul Abedin.
"They reached Dehradun on Tuesday and found the pitch a bit grassy, so we decided to send a pace bowler. Otherwise, we would have sent a spinner."
Abul's last four Twenty20 internationals were against Pakistan in 2012.