A frantic three-wicket victory sealed on Monday gave Bangladesh a 1-0 lead in the three-match series, but seamer Hossain's contribution in Dhaka was limited.
Having bowled just eight overs in the first innings at the cost of 22 runs, he was unused in the second as Taijul Islam ripped through the Zimbabwe batting order with 8-39.
Hossain was reported to the International Cricket Council (ICC) for a suspected bowling action last month during a 10-wicket loss to West Indies in St Lucia.
Haque, a wicketkeeper-batsman, is due to join the 14-man squad later this week, ahead of the start of the second Test in Khulna, which begins on November 3.
The 21-year-old has struggled to contribute with the bat in four Test appearances since making his debut in March 2013 and currently only averages 9.12 from his eight innings.
Victory for Bangladesh in the next match would see them secure a first Test series win since 2009, when they beat West Indies 2-0.