Shakib hit an unbeaten 70 off 45 balls to guide Bangladesh to 139-6 in 19 overs after young off-spinner Afif Hossain led the bowling effort with 2-9.
Captain Masakadza hit 71 off 42 balls with four fours and five sixes as Zimbabwe reached a target of 156 with three balls to spare.
The hosts will face Afghanistan in the final on Tuesday in Dhaka, while Zimbabwe will finish their campaign against the same opponents on Friday.
Soumya faced criticism for his poor outings in the tournament so far, having scored just four runs in two innings including a duck.
Nabi hit an unbeaten 84 off 54 balls under pressure to guide Afghanistan to 164-6 before Mujeeb claimed a career-best 4-15.
"We have so many good players at the moment and we just need guys to jump out the box and be a lot more consistent."
Najibullah Zadran hit a blistering half-century as Afghanistan beat Zimbabwe by 28 runs in their first match of the tri-nation T20I tournament.
Afif, batting at number eight, hit eight fours and a six in his maiden international fifty that guided Bangladesh to 148-7 in 17.4 overs.
Tamim Iqbal continues to miss out after requesting a break from international cricket.
Wasim Akram, Yuvraj Singh sign up for Bushfire Cricket Bash
Pakistan Under-19 team claims a dominant win in their opening World Cup game
Bangladesh announces squad for Pakistan T20Is
Tearaway quick Haris Rauf vows to make most of opportunity
PSL digital media partner ‘Cricingif’ aims to provide you the best coverage
Mark Wood powers England into dominant position in fourth Test
Fawad Alam included in Test probables for Bangladesh clash
De Villiers will be welcomed back to South African side, says Faf du Plessis
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