The 17-year-old is expected to make his debut for Bangladesh in the four-match series beginning in Harare on February 4.
Tamim, younger brother of out-of-form Bangladesh opener Nafis Iqbal Khan, has replaced Farhad Reza, the Bangladesh Cricket Board said.
The rookie, who has played some brilliant innings in the ongoing Dhaka league, is also a likely candidate to make the team for the upcoming World Cup in the West Indies.
Medium pacers Tapash Baishya, 24, and Mohammad Sharif, 21, were recalled to the 15-man squad for Zimbabwe after fine performances in the domestic league.
Sharif last played for Bangladesh in January 2002 before he was sidelined for more than three years following an ankle injury.
Left-arm medium pacer Syed Rasel has been igonred after a poor series against Zimbabwe last month.
The selectors also ignored experienced wicket-keeper Khaled Masud for the tour. Masud, 30, is Bangladesh's second most experienced one-day player with 126 matches since making his debut in 1995.
Bangladesh will play their matches on February 4, 6, 9 and 10.
Squad: Habibul Bashar (captain), Shahriar Nafees Ahmed (vice captain), Aftab Ahmed, Mohammed Rafique, Mashrafe Mortaza, Tushar Imran, Mohammad Ashraful, Sakib Al Hasan, Mehrab Hossain, Shahadat Hossain, Mushfiqur Rahim, Mohammed Sharif, Tapash Baishya, Abdur Razzak, Tamim Iqbal Khan. Coach: Dav Whatmore.