"Nazim has torn one of the tendons on his left ring finger during the pre-match warm up of the practice game against the Australian Institute of Sports in Darwin today," it said in a statement.
"The injury would require six to eight weeks of immobilization in a splint," it said. He will fly home and the team management has asked for a replacement.
The 23-year-old batsman, who has scored just 90 runs in seven one-day internationals, was included only after fellow opener Shahriar Nafees opted out to attend exams.
Bangladesh play five warm-up matches ahead of the series, to be played in Darwin on Aug 30, Sept 3 and 6.