Around 4:30pm on Wednesday, one bike was set on fire in the southeast corner of Eidgah, one in front of the Eidgah main gate and one in front of the Bar Council, according to eyewitnesses.
No one was seen at the scene during the incident.
Later, firefighters came in and put out the fire, he said.
Police are investigating the matter, said Ramna Division Deputy Commissioner Sajjadur Rahman.
The law enforcers heightened security in the Supreme Court area ahead of the hearing after a group of her supporters clashed with police on Nov 26 in the same area demanding her release.
Lawyers for the BNP chief created a chaos in the courtroom on Dec 5 when the judges deferred the hearing.
On Wednesday, more police than usual were deployed at the entrances to the court.
A water cannon was also deployed at the Matsya Bhaban intersection.