Mominul and Mahmudullah were part of Bangladesh's squad during their last series in Sri Lanka, though they did not play the final Test in Colombo, which Bangladesh won by four wickets to finish the two-match series 1-1.
"It was expected that Mahmudullah would not be in the squad because he did not play the final Test in Sri Lanka," chief selector Minhajul Abedin said in Dhaka while announcing the squad.
"Mominul also missed out the last Test match. In addition, the kind of statistics that we have, they indicate he is not in good form," said Minhajul.
Shafiul Islam also returned to the side after a good show during a recent warm-up match in Chittagong when he picked up five wickets. Subashis Roy and Rubel Hossain, who were in the Test side during the Sri Lanka series, have also been omitted.
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Australia cricket team arrived in the Bangladesh capital Friday to play two Tests against the hosts as tight security greeted Steven Smith's men at the airport.
Australia were due to play two Tests in Bangladesh in October 2015 but the tour was cancelled over security fears after a wave of attacks by Islamist extremists in the Muslim- majority nation.
Cricket Australia agreed to reschedule the series this year only after Bangladesh promised a head-of-state style security for the visitors.
Australia are scheduled to play a warm-up match on August 22-23 before they take on Bangladesh in the first Test at Sher-e Bangla National Stadium in Dhaka.
Squad: Mushfiqur Rahim (c), Tamim Iqbal, Soumya Sarkar, Imrul Kayes, Liton Das, Shakib Al Hasan, Mosaddek Hossain, Nasir Hossain, Sabbir Rahman, Mehedi Hasan, Shafiul Islam, Taijul Islam, Mustafizur Rahman and Taskin Ahmed.
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