The killing marks the first attack by the terror group in Bangladesh.
Cesare Tavella was shot Monday night after three people rode beside him on a motorbike.
Mr Tavella, who was a vetinary surgeon in his 50s, had been living alone in the capital, Dhaka, after arriving in the country in May.
He had been working for a church-based organisation in the Netherlands, according to his colleague Alo Rani Dhali.
Police have no leads on who the attackers are, according to The Guardian.
It is estimated that around 90% of Bangladeshis are Muslim.
In a statement IS said a 'security detachment' had killed him with 'silenced weapons'.
It also warned that 'citizens of the crusader coalition' would not be safe in Muslim countries.
