Blessing Muzarabani removed Tamim Iqbal for a duck, say on Friday in the first ODI of the three-match series in Harare.
Zimbabwe won the toss and opted to bowl first.
Bangladesh failed to score even a single in the first two overs. Off the first ball of the third over, Tamim went to cut but managed only an edge to the wicketkeeper.
Shakib Al Hasan came in at number three and hit a four off the first ball he faced.
Bangladesh are missing the service of Mushfiqur Rahim who came home abruptly from this series after his parents tested positive for Covid-19.
The second and third ODI will take place on July 18 and 20 at the same venue.
After ODIs, both the teams will lock horns in a three-match T20I series.
Before the limited-over series, Bangladesh won the one-off Test against the hosts by 220 runs.
Bangladesh (Playing XI): Tamim Iqbal (c), Liton Das (w), Mohammad Mithun, Mosaddek Hossain, Shakib Al Hasan, Mahmudullah, Mehidy Hasan, Mohammad Saifuddin, Afif Hossain, Taskin Ahmed, Shoriful Islam
Zimbabwe (Playing XI): Wesley Madhevere, Tadiwanashe Marumani, Brendan Taylor (c), Dion Myers, Timycen Maruma, Regis Chakabva (w), Ryan Burl, Luke Jongwe, Tendai Chatara, Blessing Muzarabani, Richard Ngarava.