The move follows the Indian cricket board's decision to have Kolkata Knight Riders drop Bangladesh pacer Mustafizur Rahman, who had signed for the IPL franchise for this season.
Bangladesh have also refused to play their matches of next month's Twenty20 World Cup in India, demanding those be staged in Sri Lanka, co-host of the 20-team tournament.
The unceremonious dumping of a "star player" like Mustafizur from the IPL "defied logic" and had "hurt people", the country's Ministry of Information and Broadcasting said in a statement explaining its decision.
The IPL, the world's richest T20 league, is scheduled from March 26th to May 31st.
The International Cricket Council (ICC) did not reply to Reuters emails inquiring whether it would agree to Bangladesh's demand to play their World Cup matches in Sri Lanka.
Tensions have risen in recent weeks between India and Bangladesh.
Hundreds protested near Bangladesh's High Commission in New Delhi last month after a Hindu factory worker was beaten and set on fire in Bangladesh's Mymensingh district over allegations he insulted the Prophet Muhammad.
Following the protests, the Indian board asked Knight Riders to drop Mustafizur.