A hearing for the explosive case related to the 2009 Pilkhana BDR carnage was scheduled for 10:30am on Thursday but was postponed due to the damage.
The prosecutor announced that the new hearing date would be set later in the day.
According to fire service officials, they received reports of the fire at 3:10am and were blocked by protesters when they attempted to extinguish it.
They returned in the morning to find the courtroom burned.
The Alia Madrasa students have been protesting against the use of their campus for court proceedings, demanding its relocation.
On Wednesday night, they blocked the roads, ending the 10-hour demonstration at 11am on Thursday.
The 2009 BDR carnage at Pilkhana resulted in the deaths of 74 people, including 57 military officers.
Separate cases were filed for murder and explosives on February 28, 2009.
The murder case has been adjudicated, but testimony in the explosives case is ongoing.
Protests have been ongoing, with dismissed BDR members and their families demanding retrial, justice, reinstatement and rehabilitation.
On Thursday, they continued demonstrations with a "Shahbagh Blockade" program.
Chawk Bazar Police Station Officer-in-Charge Md Rezaul Hossain said that the courtroom gates were locked and only light smoke was visible in the morning.
Fire service personnel later declared the fire extinguished.