Sakib Al Hasan and Forhad Reza were named in the squad after outstanding performances with the Bangladesh youth teams over the past year, chief selector Faruq Ahmed told AFP on Monday.
Hasan is a left arm spinner and a middle order batsman who had an outstanding season with the Bangladesh under-19 squad.
Forhad Reza, a middle order batsman and a seamer, was the top scorer in last year's domestic cricket league.
"They are very good cricketers in all departments of the game. We have high hopes from them and it's time for them to perform at the international level," said Ahmed.
Middle order batsman Tushar Imran and left arm spinner Abdur Razzak were dropped from the side that also sees the return of young middle order batsman Mushfiqur Rahim.
Bangladesh, who beat Kenya 4-0 in a one-day series at home early this year, will leave for Nairobi on July 16. They will play three one-day matches against Kenya on July 19, 22 and 23.
Habibul Bashar's team will also play five one-dayers against Zimbabwe on July 29 and 30 and August 2, 4 and 6.
The squad: Habibul Bashar (capt), Mohammad Ashraful, Shahriar Nafees, Rajin Saleh, Javed Omar, Aftab Ahmed, Mushfiqur Rahim, Khaled Mashud, Mohammad Rafique, Mashrafee Bin Mortaza, Syed Rasel, Shahadat Hossain, Forhad Reza, Sakib Al Hasan, Alok Kapali