Middle-order Sabbir and opener Anamul paid the price for poor performances during Bangladesh's win over the West Indies in a three-match one-day international series last month.
Sabbir, who concluded a six-month ban from domestic cricket in June for assaulting a fan, accumulated just 27 runs in the series while Anamul made 33.
"Sabbir's form is really bad, so it was difficult to keep him in the squad. His selection had nothing to do with his disciplinary problems," Bangladesh Cricket Board (BCB)'s chief selector Minhajul Abedin said.
"We dropped Anamul as he could not fulfil our expectations in West Indies," he added.
All-rounder Ariful Haque and wicketkeeper-batsman Mohammad Mithun were picked instead for the squad.
Ariful has played six Twenty20 internationals but is yet to make his debut in other formats. Mithun is being recalled after playing the last of three ODIs against Sri Lanka earlier this year.
"We need someone who can bat at six to seven (order). Mithun is an option for this. Ariful is also playing well in domestic cricket recently," said Abedin.
Vice-captain Shakib al Hasan will feature despite suggestions he would miss the tournament due to an injured finger.
Bangladesh are in Pool B in the Asia Cup alongside Sri Lanka and Afghanistan.
The tournament, which includes regional powerhouses like India, Pakistan and a qualifier, will run from September 15 to 28.
Squad: Mashrafe Mortaza (Capt), Shakib Al Hasan, Tamim Iqbal, Mohammad Mithun, Liton Kumar, Mushfiqur Rahim, Ariful Haque, Mahmudullah Riyad, Mosaddek Hossain, Nazmul Hossain, Mehedi Hasan, Nazmul Islam, Rubel Hossain, Mustafizur Rahman and Abu Haider.
First Published: August 30, 2018, 6:51 PM IST