Mushfiq opted out of the West Indies tour to make the Hajj pilgrimage but will return for the One-Day International (ODI) series that follows in Zimbabwe.
Bangladesh will be without Tamim Iqbal following his retirement from T20Is, but the experienced opening batsman is due to captain the ODI squad.
“We are lagging behind in Tests and T20s compared to ODIs. It is important for us we improve,” Nurul said last week in Dhaka.
“For me fearless cricket is important. We will see if we can do this,” he added.
“If we remain fearless, the chances for things turning positive will be high. When you have fear of failure it will affect you negatively.”
Pace bowler Hasan Mahmud, who last played an international match 16 months ago, was included in both the T20 and ODI squads after regaining full fitness from injury.
Uncapped opener Parvez Hossain has been called up, while Mehidy Hasan, a Test and ODI regular, could also feature in the T20 matches on 30-31 July and 2 August.
Zimbabwe rebounded from two disastrous white-ball series at home to Afghanistan by clinching a spot at the Twenty20 World Cup for the first time since 2016.
A pair of 3-0 losses in both ODI and T20 series cost Lalchand Rajput his job, with former star Zimbabwe batsman Dave Houghton returning for a second spell as coach.
Zimbabwe won all five matches in the qualifying tournament under Houghton in Bulawayo, and aim to the use the upcoming visits of Bangladesh and India, who tour in August, as preparation for the World Cup later this year in Australia.
“It is very exciting because now we are looking forward to something,” Zimbabwe all-rounder Sikandar Raza told ESPNcricinfo.
“Everything we do now is a build-up to Australia. We want to be in the main tournament. We want to cause a few upsets.
“We are trying to beat all these teams so that we can form a culture, so that when we get to Australia, we have a winning changing room.”
Zimbabwe seamer Tendai Chatara risks missing the World Cup after fracturing his collarbone, while fellow bowler Blessing Muzarabani is sidelined with a muscle problem.
Victor Nyauchi and Brad Evans were named as replacements. Both made their international T20 debuts in May but neither have played an ODI.
All the matches will be held at the Harare Sports Club ground, with the ODIs -- which are not part of the World Cup Super League -- scheduled for 5, 7 and 10 August.