Ricky Ponting's team, who won the first Test by three wickets, are on their first full tour of Bangladesh.
Imran, captain of the Bangladesh A team, has been called up after he performed well against the touring Sri Lankans earlier this month, chief selector Faruq Ahmed said.
"He had a fine series against Sri Lanka A. We have called him to strengthen our middle order batting," he said Wednesday.
Imran, dropped from the national squad after Bangladesh's tour of Sri Lanka in August last year, replaces all-rounder Manzrul Islam Rana in the 14-man squad.
Bangladesh, who beat Kenya 4-0 in a one-day series at home, have had creditable one-day performances in recent months, including a shock victory over world champions Australia last year in England.
The first one-dayer will be played at Chittagong stadium on April 23 followed by two one-dayers at Fatullah stadium near Dhaka on April 26 and 28.
Squad: Habibul Bashar (capt), Khaled Mashud (vice capt), Javed Omar, Mohammad Rafique, Rajin Saleh, Mohammad Ashraful, Mashrafee Bin Mortaza, Aftab Ahmed, Tushar Imran, Abdur Razzak, Alok Kapali, Shahriar Nafees, Shahadat Hossain, Syed Rasel.