Jaishankar was received at the airport by his counterpart Md Sjajidul Haque, Indian High Commissioner Harsh Vardhan Shringla and other high officials.
Soon after his arrival he called on Prime Minister Sheikh Hasina at her official residence Gano Bhaban. He will also meet Foreign Minister AH Mahmood Ali.
Diplomatic sources said Jaishankar is expected to convey New Delhi's full support to Bangladesh on countering violent extremism amid spreading of terrorist acts in recent months.
His visit assumes significance in the backdrop of the recent killings of bloggers, secular activists and teachers, as well as the overall security situation in Bangladesh and South Asia.