Mushfiqur and Liton missed Bangladesh’s stunning 4-1 T20 thrashing of Australia earlier this month because of Covid-19 rules.
Opening batsman Tamim Iqbal, who was also absent from the Australia series due to a knee injury, has been left out as he is yet to recover fully.
Batsman Mohammad Mithun was dropped and Bangladesh added leg-spinner Aminul Islam Biplob to the squad.
The Black Caps arrive in Dhaka on August 24 for the series which comes ahead of the T20 World Cup in October and November in the United Arab Emirates and Oman.
The matches will be held behind closed doors on September 1, 3, 5, 8 and 10 at the Sher-e-Bangla National Stadium in Dhaka.