Rahane will be in charge for three one-day internationals and a pair of Twenty20 games after India opted to rest a number of stars, including regular captain MS Dhoni.
Virat Kohli, Rohit Sharma, Ravichandran Ashwin, Shikhar Dhawan, Ravindra Jadeja and Umesh Yadav were also omitted from their tour party.
Veteran off-spinner Harbhajan Singh, who turns 35 on Friday, was included in the 15-man squad even though he has not played one-day cricket for India since 2011 and Twenty20 matches since 2012.
Murali Vijay, Robin Uthappa and Manoj Tiwary were handed recalls while seamer Sandeep Sharma and batsman Manish Pandey are the only uncapped players in the squad.
All five matches will be played in Harare, with the one-dayers scheduled for July 10, 12 and 14, and the Twenty20 games on July 17 and 19.
Squad: Ajinkya Rahane (capt), Murali Vijay, Ambati Rayudu, Manoj Tiwary, Kedar Jadhav, Robin Uthappa, Manish Pandey, Harbhajan Singh, Axar Patel, Karn Sharma, Dhawal Kulkarni, Stuart Binny, Bhuvneshwar Kumar, Mohit Sharma, Sandeep Sharma.