Akhtar is facing a disciplinary committee for criticising the Pakistan Cricket Board (PCB) over contracts while Asif faces fitness problems.
"Akhtar is due to appear before a disciplinary committee so he was not considered while Asif has not been cleared on fitness by the team management," chief selector Salahuddin Ahmed said.
The 32-year-old Akhtar appears before a PCB disciplinary committee on Tuesday. He faces charges of violating the code of conduct by criticising the board.
Akhtar accused the PCB of "dual standards" in awarding the players' central contract from which he was left out. He was instead given a retainer's contract which he refused to accept.
The 25-year-old Asif has not played since featuring in the one-day series against South Africa in October last year. He suffered an elbow injury which was operated on in Australia in December.
Paceman Umar Gul was named to the squad after recovering from back trouble which forced him to leave the tour of India in November last year.
Ahmed said the 16-man squad is for the first two matches.
"We will give chance to all the players who have been doing well in the domestic competitions," said Ahmed.
Bangladesh arrive here on April 6 and play the first of five matches in Lahore two days later.
The remaining matches will be played in Faisalabad (April 11), Lahore (April 13), Multan (April 16) and Karachi (April 19).
The tourists will also play a Twenty20 international in Karachi on April 20.
PCB arranged the one-day series against Bangladesh to fill the gap created by the postponement of Australia's tour. Australia postponed their March-April tour over security fears.
Squad: Shoaib Malik (captain), Salman Butt, Nasir Jamshed, Younis Khan, Misbah-ul Haq, Mohammad Yousuf, Shahid Afridi, Kamran Akmal, Umar Gul, Sohail Tanveer, Rao Iftikhar, Sohail Khan, Wahab Riaz, Fawad Alam, Bazid Khan, Sarfraz Ahmed.