Rohit missed India's 188-run victory in the first test after sustaining a blow to the thumb during the preceding ODI series.
"The medical team is of the opinion that the injury needs some more time to heal completely before the Indian captain can bat and field with full intensity," the BCCI said in a statement.
"He will continue his rehab and will not be available for the second and final test against Bangladesh.
"Navdeep Saini is also ruled out of the second test owing to an abdominal muscle strain."
KL Rahul, who captained India in the first test, will continue as stand-in skipper.
The second test begins on Thursday in Mirpur.
Squad:
KL Rahul (capt), Shubman Gill, Cheteshwar Pujara, Virat Kohli, Shreyas Iyer, Rishabh Pant, KS Bharat, Ravichandran Ashwin, Axar Patel, Kuldeep Yadav, Shardul Thakur, Mohammed Siraj, Umesh Yadav, Abhimanyu Easwaran, Saurabh Kumar, Jaydev Unadkat.
