The 35-year old played his last Test against Zimbabwe in Harare in July this year with Bangladesh recording a 220-run win.
Mushfiqur was under fire for his below-par performance in the recent Twenty20 World Cup, having scored just one half-century in eight matches.
T20 World Cup 2021: 'We were just not good enough', admits Mahmudullah after Scotland shock Bangladesh
The loss against Scotland hurt Bangladesh's chances of moving into the Super 12 stage.
Bangladesh vs New Zealand: Mahmudullah Riyad hits unbeaten 43 as hosts win by six wickets to claim T20I series
New Zealand were bowled out for 93 and Bangladesh captain Mahmudullah Riyad hit an unbeaten 43 as his side reached 96 for four with five balls to spare. Victory gave Bangladesh an unbeatable 3-1 series lead.
Bangladesh vs New Zealand: Ajaz Patel, Cole McConchie star as visitors win third T20I to stay alive in series
Left-arm spinner Ajaz Patel claimed a career-best 4-16 as New Zealand bowled out Bangladesh for 76 in 19.3 overs after posting a modest 128-5 when they elected to bat first.
Opener Mohammad Naim scored 39 and put on 59 for the first wicket with Liton Das (33) to lay the foundation for Bangladesh's 141 for six off 20 overs. Skipper Mahmudullah Riyad remained unbeaten on 37 at the end.
Follow all the live scores and updates of the 1st T20I between Bangladesh and New Zealand at Dhaka
Latham will lead a second-string New Zealand side with none of the players in the squad selected to play for their country in the T20 World Cup in October-November.
Set a challenging 194 to triumph, the tourists reached the target with four balls to spare when middle-order batsman Shamim Hossain hit a single.
Zimbabwe vs Bangladesh: Mohammad Naim, Soumya Sarkar set up visitors’ eight-wicket win in first T20I
Zimbabwe won the toss, chose to bat and were bowled out for 152 in 19 overs. Bangladesh reached the target with seven balls to spare to register their 33rd win from exactly 100 T20 internationals.
Highlights, Zimbabwe vs Bangladesh, 1st T20I at Harare, Full Cricket Score: Visitors win by eight wickets
Catch the live score and updates from the 1st T20I between Zimbabwe and Bangladesh on our blog.
Zimbabwe vs Bangladesh: Tamim Iqbal defies pain to score century as visitors complete 3-0 ODI series cleansweep
After scoring 20 and being out for a duck in the first two matches, Tamim let loose at the third attempt, scoring at a rate of more than a run a ball to record his 14th ODI century.
Zimbabwe vs Bangladesh: Liton Das, Shakib al Hasan's performances power visitors to 155-run win in first ODI
The tourists made 276-9 off 50 overs before left-arm spinner Shakib al Hasan took 5-30 as Zimbabwe slumped to a dismal 121 all out, with injured Timycen Maruma unable to bat.
It was the fifth Test victory for Bangladesh outside the country.
Zimbabwe vs Bangladesh: Mahmudullah Riyad stars with unbeaten 150 as visitors lead by 354 runs on Day 2 of one-off Test
In reply to Bangladesh, Zimbabwe were 114/1 in their first innings at the close of play on the second day with opening batsman Milton Shumba making 41 and captain Brendan Taylor unbeaten on 37.
The national Twenty20 skipper makes a return to the Test team after 16 months, having played his last Test in February 2020 against Pakistan.
Bangladesh vs Sri Lanka: Dushmantha Chameera, Kusal Perera star as visitors claim consolation win in third ODI
Perera's sixth ODI century and an unbeaten 55 by Dhananjaya de Silva guided Sri Lanka to 286-6, a total they defended by bowling out Bangladesh for 189 in 42.3 overs in Dhaka. The hosts won the series 2-1.
Shakib skipped the country's previous ODI series in New Zealand when his wife gave birth and also took a break from a Test tour in Sri Lanka in April to play in the lucrative Indian Premier League.
The all-rounder was scheduled to fly to Pakistan via Dubai on Sunday night, but he has instead gone into self-isolation after his COVID-19 tests returned positive.
Before the next pink ball Test is played in India, the BCCI needs to do a rethink on various issues that will make the game a little less dangerous for the players and more enjoyable for the paying spectator.