The 16-team tourney will be staged between March 16-April 6 and is considered to be the biggest ever sporting event organized by the country. (Agencies)
"If this situation prevails, then any big tournament or participation of any big country will be under threat," cricket board president Nazmul Hassan told reporters.
Seventy four people have been killed so far in violent protests with opposition supporters insisting that PM Sheikh Hasina step down with elections due next year.
"This must end in January and preferably in December," Hassan added.
The political violence has affected almost every city in Bangladesh, including the three host venues for the T20 tournament -- the capital Dhaka, Chittagong and Sylhet.
A team of International Cricket Council (ICC) inspectors declared last week that they were "happy" with security arrangements but said they would continue to monitor the situation.
Bangladesh is also due to host a tour by Sri Lanka in January before then staging the Asia Cup, a 50-over tournament starting in February which also features India, Pakistan and Sri Lanka.
"The quicker this political situation improves the better because the Sri Lanka tour is in January and then we have the Asia Cup. It needs to be resolved before that," said Hassan, who is a ruling party lawmaker.
Nizamuddin Chowdhury, the BCB's chief executive, told reporters that the ICC had asked the board to relay them an update on the situation.
The 16-team tourney will be staged between March 16-April 6 and is considered to be the biggest ever sporting event organized by the country.