Former captain Habibul Bashar, along with Shariar Nafees, Aftab Ahmed, Mosharraf Hossain, Farhad Reza and Dhiman Ghosh - who all have contracts with the Bangladesh Cricket Board - cited "personal reasons" in their resignation letters.
"The players only said they will not be available for the national team," Hossain said.
Bangladesh Cricket board held an urgent discussion on Sunday to discuss the resignations.
Local media reports said as many as 14 Bangladesh players could quit the national team in order to join the ICL in a newly formed team based in Bangladesh.
The Indian Cricket League is a Twenty20 competition that is not recognized by the International Cricket Council, and runs in opposition to the sanctioned Indian Premier League. Players competing in the ICL therefore face potential bans from international cricket.